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cleartomark

%%EndFont 
%%BeginFont: CMMI6
%!PS-AdobeFont-1.1: CMMI6 1.100
%%CreationDate: 1996 Jul 23 07:53:52

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMMI6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /alpha put
dup 12 /beta put
dup 17 /eta put
dup 18 /theta put
dup 59 /comma put
dup 82 /R put
dup 107 /k put
dup 108 /l put
dup 112 /p put
dup 113 /q put
readonly def
/FontBBox{11 -250 1241 750}readonly def
/UniqueXX 5087381 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /parenleftbig put
dup 1 /parenrightbig put
dup 2 /bracketleftbig put
dup 3 /bracketrightbig put
dup 8 /braceleftbig put
dup 9 /bracerightbig put
dup 10 /angbracketleftbig put
dup 11 /angbracketrightbig put
dup 12 /vextendsingle put
dup 13 /vextenddouble put
dup 16 /parenleftBig put
dup 17 /parenrightBig put
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 68 /angbracketleftBig put
dup 69 /angbracketrightBig put
dup 90 /integraldisplay put
dup 98 /hatwide put
dup 101 /tildewide put
dup 104 /bracketleftBig put
dup 105 /bracketrightBig put
dup 110 /braceleftBig put
dup 111 /bracerightBig put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueXX 5000774 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 48 /zero put
dup 49 /one put
dup 50 /two put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueXX 5000789 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: MSBM7
%!PS-AdobeFont-1.1: MSBM7 2.1
%%CreationDate: 1992 Oct 17 08:30:50

% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (MSBM7) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 67 /C put
dup 82 /R put
readonly def 
/FontBBox{0 -504 2615 1004}readonly def
/UniqueXX 5032014 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMSY6
%!PS-AdobeFont-1.1: CMSY6 1.0
%%CreationDate: 1991 Aug 15 07:21:34

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMSY6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 48 /prime put
dup 49 /infinity put
readonly def
/FontBBox{-4 -948 1329 786}readonly def
/UniqueXX 5000816 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMSY8
%!PS-AdobeFont-1.1: CMSY8 1.0
%%CreationDate: 1991 Aug 15 07:22:10

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 2 /multiply put
dup 3 /asteriskmath put
dup 15 /bullet put
dup 21 /greaterequal put
dup 49 /infinity put
dup 50 /element put
dup 60 /Rfractur put
dup 65 /A put
dup 66 /B put
dup 102 /braceleft put
dup 103 /braceright put
dup 110 /backslash put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueXX 5000818 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37

% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 67 /C put
dup 82 /R put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
/UniqueXX 5031982 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /Gamma put
dup 10 /Omega put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 59 /semicolon put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 100 /d put
dup 104 /h put
dup 109 /m put
dup 111 /o put
dup 116 /t put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueXX 5000791 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 1 /periodcentered put
dup 2 /multiply put
dup 20 /lessequal put
dup 21 /greaterequal put
dup 26 /propersubset put
dup 27 /propersuperset put
dup 33 /arrowright put
dup 49 /infinity put
dup 50 /element put
dup 51 /owner put
dup 55 /mapsto put
dup 56 /universal put
dup 59 /emptyset put
dup 60 /Rfractur put
dup 65 /A put
dup 66 /B put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 76 /L put
dup 79 /O put
dup 80 /P put
dup 85 /U put
dup 91 /union put
dup 92 /intersection put
dup 102 /braceleft put
dup 103 /braceright put
dup 104 /angbracketleft put
dup 105 /angbracketright put
dup 106 /bar put
dup 107 /bardbl put
dup 110 /backslash put
dup 114 /nabla put
dup 120 /section put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueXX 5000820 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMMI8
%!PS-AdobeFont-1.1: CMMI8 1.100
%%CreationDate: 1996 Jul 23 07:53:54

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /alpha put
dup 12 /beta put
dup 13 /gamma put
dup 14 /delta put
dup 17 /eta put
dup 18 /theta put
dup 58 /period put
dup 59 /comma put
dup 64 /partialdiff put
dup 66 /B put
dup 67 /C put
dup 72 /H put
dup 76 /L put
dup 77 /M put
dup 82 /R put
dup 84 /T put
dup 88 /X put
dup 89 /Y put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 112 /p put
dup 113 /q put
dup 115 /s put
dup 116 /t put
dup 120 /x put
dup 122 /z put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueXX 5087383 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMMI12
%!PS-AdobeFont-1.1: CMMI12 1.100
%%CreationDate: 1996 Jul 27 08:57:55

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /alpha put
dup 12 /beta put
dup 13 /gamma put
dup 14 /delta put
dup 17 /eta put
dup 18 /theta put
dup 20 /kappa put
dup 21 /lambda put
dup 22 /mu put
dup 23 /nu put
dup 24 /xi put
dup 30 /phi put
dup 32 /psi put
dup 39 /phi1 put
dup 44 /arrowhookleft put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 62 /greater put
dup 64 /partialdiff put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 76 /L put
dup 77 /M put
dup 81 /Q put
dup 82 /R put
dup 84 /T put
dup 85 /U put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 112 /p put
dup 113 /q put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
/UniqueXX 5087386 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMTI12
%!PS-AdobeFont-1.1: CMTI12 1.0
%%CreationDate: 1991 Aug 18 21:06:53

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMTI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /ff put
dup 12 /fi put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 52 /four put
dup 53 /five put
dup 55 /seven put
dup 58 /colon put
dup 59 /semicolon put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 72 /H put
dup 73 /I put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 124 /emdash put
readonly def
/FontBBox{-36 -251 1103 750}readonly def
/UniqueXX 5000829 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 59 /comma put
dup 62 /greater put
dup 112 /p put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueXX 5087385 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMBX10
%!PS-AdobeFont-1.1: CMBX10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 65 /A put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 114 /r put
dup 115 /s put
dup 116 /t put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueXX 5000768 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMBX12
%!PS-AdobeFont-1.1: CMBX12 1.0
%%CreationDate: 1991 Aug 20 16:34:54

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMBX12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 8 /Phi put
dup 12 /fi put
dup 25 /germandbls put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 65 /A put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 72 /H put
dup 73 /I put
dup 76 /L put
dup 78 /N put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 87 /W put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 123 /endash put
dup 127 /dieresis put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
/UniqueXX 5000769 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMCSC10
%!PS-AdobeFont-1.1: CMCSC10 1.0
%%CreationDate: 1991 Aug 18 17:46:49

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMCSC10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMCSC10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 49 /one put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 65 /A put
dup 67 /C put
dup 71 /G put
dup 72 /H put
dup 74 /J put
dup 75 /K put
dup 78 /N put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 121 /y put
dup 127 /dieresis put
readonly def
/FontBBox{14 -250 1077 750}readonly def
/UniqueXX 5000772 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMTI10
%!PS-AdobeFont-1.1: CMTI10 1.00B
%%CreationDate: 1992 Feb 19 19:56:16

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMTI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 46 /period put
dup 48 /zero put
dup 50 /two put
dup 67 /C put
dup 75 /K put
dup 77 /M put
dup 83 /S put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 119 /w put
dup 121 /y put
readonly def
/FontBBox{-163 -250 1146 969}readonly def
/UniqueXX 5000828 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 49 /one put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueXX 5000790 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 25 /germandbls put
dup 39 /quoteright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 57 /nine put
dup 58 /colon put
dup 64 /at put
dup 65 /A put
dup 66 /B put
dup 68 /D put
dup 69 /E put
dup 71 /G put
dup 73 /I put
dup 75 /K put
dup 77 /M put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 87 /W put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 123 /endash put
dup 127 /dieresis put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueXX 5000793 def
currentdict end
currentfile eexec
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cleartomark

%%EndFont 
%%BeginFont: CMR12
%!PS-AdobeFont-1.1: CMR12 1.0
%%CreationDate: 1991 Aug 20 16:38:05

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights 
Reserved) readonly def
/FullName (CMR12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /Gamma put
dup 3 /Lambda put
dup 8 /Phi put
dup 10 /Omega put
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 25 /germandbls put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 64 /at put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 124 /emdash put
dup 127 /dieresis put
readonly def
/FontBBox{-34 -251 988 750}readonly def
/UniqueXX 5000794 def
currentdict end
currentfile eexec
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1385 204 S M
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1385 204 S M
1462 198 L
1308 206 S M
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1308 206 S M
1385 204 L
1231 207 S M
1231 63 L
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1077 207 S M
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769 207 S M
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692 207 S M
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615 207 S M
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538 63 L
538 207 S M
615 207 L
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461 206 S M
538 207 L
384 203 S M
384 62 L
384 203 S M
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307 194 S M
307 60 L
307 194 S M
384 203 L
230 168 S M
230 55 L
230 168 S M
307 194 L
153 113 S M
153 46 L
153 113 S M
230 168 L
76 82 S M
76 39 L
76 82 S M
153 113 L
0 69 S M
0 34 L
0 69 S M
76 82 L
5234 104 S M
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5157 131 S M
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5080 249 S M
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5003 668 S M
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4926 707 S M
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4233 198 L
4233 709 S M
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4156 679 S M
4156 180 L
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4233 709 L
4079 310 S M
4079 134 L
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4156 679 L
4002 200 S M
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4079 310 L
3925 169 S M
3925 99 L
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3848 169 S M
3848 99 L
3848 169 S M
3925 169 L
3771 200 S M
3771 108 L
3771 200 S M
3848 169 L
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3771 200 L
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3694 310 L
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3540 190 L
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3617 679 L
3463 679 S M
3463 177 L
3463 679 S M
3540 705 L
3386 311 S M
3386 134 L
3386 311 S M
3463 679 L
3309 202 S M
3309 109 L
3309 202 S M
3386 311 L
3233 171 S M
3233 99 L
3233 171 S M
3309 202 L
3156 171 S M
3156 99 L
3156 171 S M
3233 171 L
3079 202 S M
3079 109 L
3079 202 S M
3156 171 L
3002 311 S M
3002 134 L
3002 311 S M
3079 202 L
2925 679 S M
2925 177 L
2925 679 S M
3002 311 L
2848 705 S M
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2848 705 S M
2925 679 L
2771 679 S M
2771 177 L
2771 679 S M
2848 705 L
2694 311 S M
2694 134 L
2694 311 S M
2771 679 L
2617 201 S M
2617 109 L
2617 201 S M
2694 311 L
2540 171 S M
2540 99 L
2540 171 S M
2617 201 L
2463 171 S M
2463 99 L
2463 171 S M
2540 171 L
2386 201 S M
2386 109 L
2386 201 S M
2463 171 L
2309 311 S M
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2309 311 S M
2386 201 L
2232 679 S M
2232 177 L
2232 679 S M
2309 311 L
2155 705 S M
2155 190 L
2155 705 S M
2232 679 L
2078 679 S M
2078 177 L
2078 679 S M
2155 705 L
2001 311 S M
2001 134 L
2001 311 S M
2078 679 L
1924 202 S M
1924 109 L
1924 202 S M
2001 311 L
1847 171 S M
1847 99 L
1847 171 S M
1924 202 L
1770 171 S M
1770 99 L
1770 171 S M
1847 171 L
1693 202 S M
1693 109 L
1693 202 S M
1770 171 L
1616 311 S M
1616 134 L
1616 311 S M
1693 202 L
1539 680 S M
1539 180 L
1539 680 S M
1616 311 L
1462 709 S M
1462 198 L
1462 709 S M
1539 680 L
1385 712 S M
1385 204 L
1385 712 S M
1462 709 L
1308 713 S M
1308 206 L
1308 713 S M
1385 712 L
1231 713 S M
1231 207 L
1231 713 S M
1308 713 L
1154 713 S M
1154 207 L
1154 713 S M
1231 713 L
1077 713 S M
1077 207 L
1077 713 S M
1154 713 L
1000 713 S M
1000 207 L
1000 713 S M
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923 713 S M
923 207 L
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1000 713 L
846 713 S M
846 207 L
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769 713 S M
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692 713 S M
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615 713 S M
615 207 L
615 713 S M
692 713 L
538 713 S M
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538 713 S M
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538 713 L
384 711 S M
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307 707 S M
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230 668 S M
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230 668 S M
307 707 L
153 249 S M
153 113 L
153 249 S M
230 668 L
76 131 S M
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76 131 S M
153 249 L
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0 69 L
0 104 S M
76 131 L
5234 138 S M
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5234 138 L
5080 647 S M
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5080 647 S M
5157 187 L
5003 821 S M
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4618 713 L
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4156 821 S M
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4079 310 L
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4156 821 L
4002 327 S M
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4079 703 L
3925 257 S M
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3925 257 S M
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3848 258 S M
3848 169 L
3848 258 S M
3925 257 L
3771 328 S M
3771 200 L
3771 328 S M
3848 258 L
3694 703 S M
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3694 703 S M
3771 328 L
3617 821 S M
3617 678 L
3617 821 S M
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3540 821 S M
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3540 821 S M
3617 821 L
3463 821 S M
3463 679 L
3463 821 S M
3540 821 L
3386 705 S M
3386 311 L
3386 705 S M
3463 821 L
3309 333 S M
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3233 262 S M
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3233 262 S M
3309 333 L
3156 262 S M
3156 171 L
3156 262 S M
3233 262 L
3079 333 S M
3079 202 L
3079 333 S M
3156 262 L
3002 705 S M
3002 311 L
3002 705 S M
3079 333 L
2925 821 S M
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2925 821 S M
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2848 821 S M
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2848 821 S M
2925 821 L
2771 821 S M
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2694 704 S M
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2771 821 L
2617 332 S M
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2540 262 S M
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2540 262 L
2386 332 S M
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2386 332 S M
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2386 332 L
2232 821 S M
2232 679 L
2232 821 S M
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2155 821 S M
2155 705 L
2155 821 S M
2232 821 L
2078 821 S M
2078 679 L
2078 821 S M
2155 821 L
2001 704 S M
2001 311 L
2001 704 S M
2078 821 L
1924 332 S M
1924 201 L
1924 332 S M
2001 704 L
1847 262 S M
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1770 262 S M
1770 171 L
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1693 332 S M
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1693 332 S M
1770 262 L
1616 705 S M
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1539 821 S M
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1539 821 S M
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1462 821 S M
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1462 821 S M
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1385 821 S M
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1385 821 S M
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1308 821 S M
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1308 821 S M
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1231 821 S M
1231 713 L
1231 821 S M
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1154 821 S M
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1231 821 L
1077 821 S M
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1154 821 L
1000 821 S M
1000 713 L
1000 821 S M
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923 821 S M
923 713 L
923 821 S M
1000 821 L
846 821 S M
846 713 L
846 821 S M
923 821 L
769 821 S M
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769 821 S M
846 821 L
692 821 S M
692 713 L
692 821 S M
769 821 L
615 821 S M
615 713 L
615 821 S M
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538 821 S M
538 713 L
538 821 S M
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461 821 S M
538 821 L
384 821 S M
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384 821 S M
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307 821 S M
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230 821 S M
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153 647 S M
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153 647 S M
230 821 L
76 187 S M
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76 187 S M
153 647 L
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0 104 L
0 138 S M
76 187 L
5234 173 S M
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5080 744 S M
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4926 855 S M
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4156 855 S M
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4079 800 S M
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4079 800 S M
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4002 438 S M
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4002 438 S M
4079 800 L
3925 348 S M
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3925 348 S M
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3848 350 S M
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3848 350 S M
3925 348 L
3771 443 S M
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3771 443 S M
3848 350 L
3694 801 S M
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3694 801 S M
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3617 855 S M
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3617 855 S M
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3540 855 S M
3540 821 L
3540 855 S M
3617 855 L
3463 855 S M
3463 821 L
3463 855 S M
3540 855 L
3386 802 S M
3386 704 L
3386 802 S M
3463 855 L
3309 452 S M
3309 333 L
3309 452 S M
3386 802 L
3233 360 S M
3233 262 L
3233 360 S M
3309 452 L
3156 360 S M
3156 262 L
3156 360 S M
3233 360 L
3079 452 S M
3079 333 L
3079 452 S M
3156 360 L
3002 802 S M
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3002 802 S M
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2925 855 S M
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2848 855 S M
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2848 855 S M
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2771 855 S M
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2771 855 S M
2848 855 L
2694 802 S M
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2694 802 S M
2771 855 L
2617 451 S M
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2617 451 S M
2694 802 L
2540 359 S M
2540 262 L
2540 359 S M
2617 451 L
2463 359 S M
2463 262 L
2463 359 S M
2540 359 L
2386 451 S M
2386 332 L
2386 451 S M
2463 359 L
2309 802 S M
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2309 802 S M
2386 451 L
2232 855 S M
2232 821 L
2232 855 S M
2309 802 L
2155 855 S M
2155 821 L
2155 855 S M
2232 855 L
2078 855 S M
2078 821 L
2078 855 S M
2155 855 L
2001 802 S M
2001 704 L
2001 802 S M
2078 855 L
1924 451 S M
1924 332 L
1924 451 S M
2001 802 L
1847 359 S M
1847 262 L
1847 359 S M
1924 451 L
1770 359 S M
1770 262 L
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1693 451 S M
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1693 451 S M
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1616 802 S M
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1616 802 S M
1693 451 L
1539 855 S M
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1539 855 S M
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1462 855 S M
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1462 855 S M
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1385 855 S M
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1385 855 S M
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1154 855 S M
1231 855 L
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1077 855 S M
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1000 855 S M
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1000 855 S M
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923 856 S M
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1000 855 L
846 855 S M
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846 855 L
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692 855 S M
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615 855 S M
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615 855 S M
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538 855 S M
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538 855 S M
615 855 L
461 855 S M
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461 855 S M
538 855 L
384 855 S M
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384 855 S M
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307 855 S M
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307 855 S M
384 855 L
230 855 S M
230 820 L
230 855 S M
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153 744 S M
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153 744 S M
230 855 L
76 233 S M
76 187 L
76 233 S M
153 744 L
0 173 S M
0 138 L
0 173 S M
76 233 L
5234 208 S M
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5157 272 S M
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5234 208 L
5080 786 S M
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5080 786 S M
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5003 890 S M
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4926 890 S M
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4926 890 S M
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4926 890 L
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4541 890 L
4387 890 S M
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4156 890 L
4002 519 S M
4002 438 L
4002 519 S M
4079 844 L
3925 427 S M
3925 348 L
3925 427 S M
4002 519 L
3848 432 S M
3848 350 L
3848 432 S M
3925 427 L
3771 532 S M
3771 443 L
3771 532 S M
3848 432 L
3694 848 S M
3694 801 L
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3771 532 L
3617 890 S M
3617 855 L
3617 890 S M
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3540 890 S M
3540 855 L
3540 890 S M
3617 890 L
3463 890 S M
3463 855 L
3463 890 S M
3540 890 L
3386 850 S M
3386 802 L
3386 850 S M
3463 890 L
3309 548 S M
3309 452 L
3309 548 S M
3386 850 L
3233 453 S M
3233 360 L
3233 453 S M
3309 548 L
3156 453 S M
3156 360 L
3156 453 S M
3233 453 L
3079 548 S M
3079 452 L
3079 548 S M
3156 453 L
3002 850 S M
3002 802 L
3002 850 S M
3079 548 L
2925 890 S M
2925 855 L
2925 890 S M
3002 850 L
2848 890 S M
2848 855 L
2848 890 S M
2925 890 L
2771 890 S M
2771 855 L
2771 890 S M
2848 890 L
2694 850 S M
2694 802 L
2694 850 S M
2771 890 L
2617 546 S M
2617 450 L
2617 546 S M
2694 850 L
2540 449 S M
2540 359 L
2540 449 S M
2617 546 L
2463 449 S M
2463 359 L
2463 449 S M
2540 449 L
2386 546 S M
2386 450 L
2386 546 S M
2463 449 L
2309 850 S M
2309 802 L
2309 850 S M
2386 546 L
2232 890 S M
2232 855 L
2232 890 S M
2309 850 L
2155 890 S M
2155 855 L
2155 890 S M
2232 890 L
2078 890 S M
2078 855 L
2078 890 S M
2155 890 L
2001 850 S M
2001 802 L
2001 850 S M
2078 890 L
1924 546 S M
1924 450 L
1924 546 S M
2001 850 L
1847 449 S M
1847 359 L
1847 449 S M
1924 546 L
1770 450 S M
1770 359 L
1770 450 S M
1847 449 L
1693 546 S M
1693 451 L
1693 546 S M
1770 450 L
1616 850 S M
1616 802 L
1616 850 S M
1693 546 L
1539 890 S M
1539 855 L
1539 890 S M
1616 850 L
1462 890 S M
1462 855 L
1462 890 S M
1539 890 L
1385 890 S M
1385 855 L
1385 890 S M
1462 890 L
1308 890 S M
1308 855 L
1308 890 S M
1385 890 L
1231 890 S M
1231 855 L
1231 890 S M
1308 890 L
1154 890 S M
1154 855 L
1154 890 S M
1231 890 L
1077 890 S M
1077 855 L
1077 890 S M
1154 890 L
1000 890 S M
1000 855 L
1000 890 S M
1077 890 L
923 890 S M
923 855 L
923 890 S M
1000 890 L
846 890 S M
846 855 L
846 890 S M
923 890 L
769 890 S M
769 855 L
769 890 S M
846 890 L
692 890 S M
692 855 L
692 890 S M
769 890 L
615 890 S M
615 855 L
615 890 S M
692 890 L
538 890 S M
538 855 L
538 890 S M
615 890 L
461 890 S M
461 855 L
461 890 S M
538 890 L
384 890 S M
384 855 L
384 890 S M
461 890 L
307 890 S M
307 855 L
307 890 S M
384 890 L
230 890 S M
230 855 L
230 890 S M
307 890 L
153 786 S M
153 744 L
153 786 S M
230 890 L
76 272 S M
76 233 L
76 272 S M
153 786 L
0 208 S M
0 173 L
0 208 S M
76 272 L
5234 242 S M
5234 208 L
5157 308 S M
5157 272 L
5157 308 S M
5234 242 L
5080 822 S M
5080 786 L
5080 822 S M
5157 308 L
5003 925 S M
5003 890 L
5003 925 S M
5080 822 L
4926 925 S M
4926 890 L
4926 925 S M
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4849 890 L
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4849 925 L
4695 925 S M
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4772 925 L
4618 925 S M
4618 890 L
4618 925 S M
4695 925 L
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2001 890 S M
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2001 890 L
1847 528 S M
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76 308 S M
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3925 527 S M
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3848 548 S M
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3771 652 S M
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2540 593 S M
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2001 928 S M
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2001 928 L
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615 945 S M
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538 947 L
384 959 S M
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307 959 S M
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384 959 L
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230 959 L
76 343 S M
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76 343 S M
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0 277 S M
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0 277 S M
76 343 L
5234 312 S M
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5234 312 L
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4849 994 L
4695 946 S M
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4751 953 S M
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3925 559 S M
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3233 667 S M
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3156 667 S M
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2001 964 S M
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2001 964 L
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1154 945 S M
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1000 980 S M
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923 994 S M
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1000 980 L
846 994 S M
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846 994 S M
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769 980 S M
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846 994 L
692 947 S M
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615 945 S M
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153 892 S M
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153 892 S M
230 994 L
76 378 S M
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76 378 S M
153 892 L
0 312 S M
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0 312 S M
76 378 L
5234 347 S M
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5157 413 S M
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5234 347 L
5080 927 S M
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4926 1029 L
4772 1009 S M
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3386 1003 S M
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3309 804 S M
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3233 729 S M
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3156 729 S M
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2925 1029 S M
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2694 1000 S M
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2771 1029 L
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2694 1000 L
2540 697 S M
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2001 1000 S M
2001 964 L
2001 1000 S M
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2001 1000 L
1847 697 S M
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1462 1029 L
1308 1010 S M
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1385 1029 L
1270 952 S M
1308 1010 L
1000 1010 S M
1000 979 L
1000 1010 S M
1038 952 L
923 1029 S M
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1000 1010 L
846 1029 S M
846 994 L
846 1029 S M
923 1029 L
769 1010 S M
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846 1029 L
731 952 S M
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461 1010 S M
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499 951 L
384 1029 S M
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384 1029 S M
461 1010 L
307 1029 S M
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384 1029 L
230 1029 S M
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307 1029 L
153 927 S M
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153 927 S M
230 1029 L
76 413 S M
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76 413 S M
153 927 L
0 347 S M
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0 347 S M
76 413 L
5234 381 S M
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5157 448 S M
5157 413 L
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5080 961 S M
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4926 1064 L
4772 1043 S M
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4849 1064 L
4724 950 S M
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4002 627 S M
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3925 627 S M
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3848 667 S M
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3925 627 L
3771 775 S M
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3848 667 L
3694 1031 S M
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3617 1064 S M
3617 1029 L
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3309 862 S M
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3386 1040 L
3233 795 S M
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3233 795 S M
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3156 795 S M
3156 729 L
3156 795 S M
3233 795 L
3079 862 S M
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3156 795 L
3002 1040 S M
3002 1002 L
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3079 862 L
2925 1064 S M
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2925 1064 S M
3002 1040 L
2848 1064 S M
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2848 1064 S M
2925 1064 L
2771 1064 S M
2771 1029 L
2771 1064 S M
2848 1064 L
2694 1035 S M
2694 1000 L
2694 1035 S M
2771 1064 L
2617 821 S M
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2694 1035 L
2540 740 S M
2540 697 L
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2463 740 S M
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2386 821 S M
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2463 740 L
2309 1036 S M
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2232 1064 S M
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2155 1064 S M
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2155 1064 S M
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2078 1064 S M
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2155 1064 L
2001 1036 S M
2001 1000 L
2001 1036 S M
2078 1064 L
1924 821 S M
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2001 1036 L
1847 740 S M
1847 697 L
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1616 1035 S M
1616 1000 L
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1539 1064 S M
1539 1029 L
1539 1064 S M
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1462 1064 S M
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1385 1064 S M
1385 1029 L
1385 1064 S M
1462 1064 L
1308 1043 S M
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1308 1043 S M
1385 1064 L
1256 950 S M
1308 1043 L
1000 1043 S M
1000 1010 L
1000 1043 S M
1052 950 L
923 1064 S M
923 1029 L
923 1064 S M
1000 1043 L
846 1064 S M
846 1029 L
846 1064 S M
923 1064 L
769 1043 S M
769 1010 L
769 1043 S M
846 1064 L
718 950 S M
769 1043 L
461 1043 S M
461 1010 L
461 1043 S M
513 950 L
384 1064 S M
384 1029 L
384 1064 S M
461 1043 L
307 1064 S M
307 1029 L
307 1064 S M
384 1064 L
230 1063 S M
230 1029 L
230 1063 S M
307 1064 L
153 961 S M
153 927 L
153 961 S M
230 1063 L
76 448 S M
76 413 L
76 448 S M
153 961 L
0 381 S M
0 347 L
0 381 S M
76 448 L
5234 416 S M
5234 381 L
5157 483 S M
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5157 483 S M
5234 416 L
5080 996 S M
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5080 996 S M
5157 483 L
5003 1098 S M
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5080 996 L
4926 1098 S M
4926 1063 L
4926 1098 S M
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4849 1098 S M
4849 1063 L
4849 1098 S M
4926 1098 L
4772 1079 S M
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4849 1098 L
4697 947 S M
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4002 673 S M
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4033 685 L
3925 671 S M
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3848 709 S M
3848 666 L
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3925 671 L
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3848 709 L
3694 1066 S M
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3386 1077 S M
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3463 1098 L
3309 930 S M
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3233 874 S M
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3233 874 S M
3309 930 L
3156 874 S M
3156 795 L
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3233 874 L
3079 930 S M
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3079 930 S M
3156 874 L
3002 1077 S M
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3079 930 L
2925 1098 S M
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2848 1098 S M
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2848 1098 L
2694 1071 S M
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2694 1071 S M
2771 1098 L
2617 860 S M
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2540 780 S M
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2463 780 L
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2232 1098 S M
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2155 1098 S M
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2155 1098 S M
2232 1098 L
2078 1098 S M
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2078 1098 S M
2155 1098 L
2001 1071 S M
2001 1035 L
2001 1071 S M
2078 1098 L
1924 860 S M
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1924 860 S M
2001 1071 L
1847 780 S M
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1770 780 S M
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1308 1077 S M
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1385 1098 L
1243 950 S M
1308 1077 L
1000 1077 S M
1000 1043 L
1000 1077 S M
1066 950 L
923 1098 S M
923 1064 L
923 1098 S M
1000 1077 L
846 1098 S M
846 1064 L
846 1098 S M
923 1098 L
769 1077 S M
769 1043 L
769 1077 S M
846 1098 L
704 950 S M
769 1077 L
461 1077 S M
461 1043 L
461 1077 S M
527 950 L
384 1098 S M
384 1063 L
384 1098 S M
461 1077 L
307 1098 S M
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307 1098 S M
384 1098 L
230 1098 S M
230 1063 L
230 1098 S M
307 1098 L
153 996 S M
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153 996 S M
230 1098 L
76 483 S M
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76 483 S M
153 996 L
0 416 S M
0 381 L
0 416 S M
76 483 L
5234 451 S M
5234 416 L
5157 517 S M
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5157 517 S M
5234 451 L
5080 1031 S M
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5080 1031 S M
5157 517 L
5003 1133 S M
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5003 1133 S M
5080 1031 L
4926 1133 S M
4926 1098 L
4926 1133 S M
5003 1133 L
4849 1133 S M
4849 1098 L
4849 1133 S M
4926 1133 L
4772 1117 S M
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4772 1117 S M
4849 1133 L
4695 1023 S M
4695 946 L
4695 1023 S M
4772 1117 L
4618 980 S M
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4618 980 S M
4695 1023 L
4541 958 S M
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4618 980 L
4464 944 S M
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4002 736 S M
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4056 775 L
3925 722 S M
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3925 722 S M
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3848 755 S M
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3848 755 S M
3925 722 L
3771 857 S M
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3848 755 L
3694 1102 S M
3694 1066 L
3694 1102 S M
3771 857 L
3617 1133 S M
3617 1098 L
3617 1133 S M
3694 1102 L
3540 1133 S M
3540 1098 L
3540 1133 S M
3617 1133 L
3463 1133 S M
3463 1098 L
3463 1133 S M
3540 1133 L
3386 1117 S M
3386 1077 L
3386 1117 S M
3463 1133 L
3309 1019 S M
3309 930 L
3309 1019 S M
3386 1117 L
3233 982 S M
3233 874 L
3233 982 S M
3309 1019 L
3156 982 S M
3156 874 L
3156 982 S M
3233 982 L
3079 1019 S M
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3079 1019 S M
3156 982 L
3002 1117 S M
3002 1077 L
3002 1117 S M
3079 1019 L
2925 1133 S M
2925 1098 L
2925 1133 S M
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2848 1133 S M
2848 1098 L
2848 1133 S M
2925 1133 L
2771 1133 S M
2771 1098 L
2771 1133 S M
2848 1133 L
2694 1106 S M
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2694 1106 S M
2771 1133 L
2617 897 S M
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2694 1106 L
2540 818 S M
2540 780 L
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2463 818 S M
2463 780 L
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2540 818 L
2386 897 S M
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2463 818 L
2309 1106 S M
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2386 897 L
2232 1133 S M
2232 1098 L
2232 1133 S M
2309 1106 L
2155 1133 S M
2155 1098 L
2155 1133 S M
2232 1133 L
2078 1133 S M
2078 1098 L
2078 1133 S M
2155 1133 L
2001 1106 S M
2001 1071 L
2001 1106 S M
2078 1133 L
1924 897 S M
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1924 897 S M
2001 1106 L
1847 818 S M
1847 780 L
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1770 818 S M
1770 780 L
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1847 818 L
1693 897 S M
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1616 1105 S M
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1616 1105 S M
1693 897 L
1539 1133 S M
1539 1098 L
1539 1133 S M
1616 1105 L
1462 1133 S M
1462 1098 L
1462 1133 S M
1539 1133 L
1385 1133 S M
1385 1098 L
1385 1133 S M
1462 1133 L
1308 1111 S M
1308 1077 L
1308 1111 S M
1385 1133 L
1231 956 S M
1231 947 L
1231 956 S M
1308 1111 L
1215 947 S M
1231 956 L
1077 956 S M
1077 947 L
1077 956 S M
1093 947 L
1000 1111 S M
1000 1077 L
1000 1111 S M
1077 956 L
923 1133 S M
923 1098 L
923 1133 S M
1000 1111 L
846 1133 S M
846 1098 L
846 1133 S M
923 1133 L
769 1111 S M
769 1077 L
769 1111 S M
846 1133 L
692 956 S M
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692 956 S M
769 1111 L
676 947 S M
692 956 L
538 956 S M
538 947 L
538 956 S M
554 947 L
461 1111 S M
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461 1111 S M
538 956 L
384 1133 S M
384 1098 L
384 1133 S M
461 1111 L
307 1133 S M
307 1098 L
307 1133 S M
384 1133 L
230 1133 S M
230 1098 L
230 1133 S M
307 1133 L
153 1031 S M
153 996 L
153 1031 S M
230 1133 L
76 517 S M
76 482 L
76 517 S M
153 1031 L
0 451 S M
0 416 L
0 451 S M
76 517 L
5234 485 S M
5234 451 L
5157 552 S M
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5234 485 L
5080 1066 S M
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5080 1066 S M
5157 552 L
5003 1168 S M
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5003 1168 S M
5080 1066 L
4926 1168 S M
4926 1133 L
4926 1168 S M
5003 1168 L
4849 1168 S M
4849 1133 L
4849 1168 S M
4926 1168 L
4772 1163 S M
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4772 1163 S M
4849 1168 L
4695 1154 S M
4695 1023 L
4695 1154 S M
4772 1163 L
4618 1151 S M
4618 980 L
4618 1151 S M
4695 1154 L
4541 1149 S M
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4541 1149 S M
4618 1151 L
4464 1148 S M
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4464 1148 S M
4541 1149 L
4387 1147 S M
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4464 1148 L
4310 1146 S M
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4310 1146 S M
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4233 1143 S M
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4233 1143 S M
4310 1146 L
4156 1130 S M
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4156 1130 S M
4233 1143 L
4079 931 S M
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4156 1130 L
4002 817 S M
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4079 931 L
3925 780 S M
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3848 803 S M
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3925 780 L
3771 900 S M
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3848 803 L
3694 1137 S M
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3694 1137 S M
3771 900 L
3617 1168 S M
3617 1133 L
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3540 1168 S M
3540 1133 L
3540 1168 S M
3617 1168 L
3463 1168 S M
3463 1133 L
3463 1168 S M
3540 1168 L
3386 1163 S M
3386 1117 L
3386 1163 S M
3463 1168 L
3309 1154 S M
3309 1019 L
3309 1154 S M
3386 1163 L
3233 1151 S M
3233 982 L
3233 1151 S M
3309 1154 L
3156 1151 S M
3156 982 L
3156 1151 S M
3233 1151 L
3079 1154 S M
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3079 1154 S M
3156 1151 L
3002 1163 S M
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3002 1163 S M
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2925 1168 S M
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2848 1168 S M
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2771 1168 S M
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2848 1168 L
2694 1140 S M
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2694 1140 S M
2771 1168 L
2617 933 S M
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2694 1140 L
2540 855 S M
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2309 1140 S M
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2232 1168 S M
2232 1133 L
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2155 1168 S M
2155 1133 L
2155 1168 S M
2232 1168 L
2078 1168 S M
2078 1133 L
2078 1168 S M
2155 1168 L
2001 1140 S M
2001 1106 L
2001 1140 S M
2078 1168 L
1924 933 S M
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1924 933 S M
2001 1140 L
1847 855 S M
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1770 855 S M
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1693 933 S M
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1616 1140 S M
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1539 1168 S M
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1616 1140 L
1462 1168 S M
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1462 1168 S M
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1385 1168 S M
1385 1133 L
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1308 1145 S M
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1308 1145 S M
1385 1168 L
1231 986 S M
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1231 986 S M
1308 1145 L
1160 946 S M
1231 986 L
1077 986 S M
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1077 986 S M
1148 946 L
1000 1145 S M
1000 1111 L
1000 1145 S M
1077 986 L
923 1168 S M
923 1133 L
923 1168 S M
1000 1145 L
846 1168 S M
846 1133 L
846 1168 S M
923 1168 L
769 1145 S M
769 1111 L
769 1145 S M
846 1168 L
692 986 S M
692 956 L
692 986 S M
769 1145 L
622 946 S M
692 986 L
538 986 S M
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538 986 S M
609 946 L
461 1145 S M
461 1111 L
461 1145 S M
538 986 L
384 1168 S M
384 1133 L
384 1168 S M
461 1145 L
307 1168 S M
307 1133 L
307 1168 S M
384 1168 L
230 1168 S M
230 1133 L
230 1168 S M
307 1168 L
153 1066 S M
153 1031 L
153 1066 S M
230 1168 L
76 552 S M
76 517 L
76 552 S M
153 1066 L
0 485 S M
0 451 L
0 485 S M
76 552 L
5234 520 S M
5234 485 L
5157 586 S M
5157 552 L
5157 586 S M
5234 520 L
5080 1100 S M
5080 1065 L
5080 1100 S M
5157 586 L
5003 1202 S M
5003 1168 L
5003 1202 S M
5080 1100 L
4926 1202 S M
4926 1168 L
4926 1202 S M
5003 1202 L
4849 1202 S M
4849 1168 L
4849 1202 S M
4926 1202 L
4772 1203 S M
4772 1163 L
4772 1203 S M
4849 1202 L
4695 1203 S M
4695 1154 L
4695 1203 S M
4772 1203 L
4618 1203 S M
4618 1151 L
4618 1203 S M
4695 1203 L
4541 1203 S M
4541 1149 L
4541 1203 S M
4618 1203 L
4464 1203 S M
4464 1148 L
4464 1203 S M
4541 1203 L
4387 1203 S M
4387 1147 L
4387 1203 S M
4464 1203 L
4310 1203 S M
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4310 1203 S M
4387 1203 L
4233 1203 S M
4233 1143 L
4233 1203 S M
4310 1203 L
4156 1203 S M
4156 1130 L
4156 1203 S M
4233 1203 L
4079 1148 S M
4079 931 L
4079 1148 S M
4156 1203 L
4002 905 S M
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4002 905 S M
4079 1148 L
3925 840 S M
3925 780 L
3925 840 S M
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3848 853 S M
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3848 853 S M
3925 840 L
3771 944 S M
3771 900 L
3771 944 S M
3848 853 L
3694 1173 S M
3694 1137 L
3694 1173 S M
3771 944 L
3617 1203 S M
3617 1168 L
3617 1203 S M
3694 1173 L
3540 1203 S M
3540 1168 L
3540 1203 S M
3617 1203 L
3463 1203 S M
3463 1168 L
3463 1203 S M
3540 1203 L
3386 1203 S M
3386 1163 L
3386 1203 S M
3463 1203 L
3309 1203 S M
3309 1154 L
3309 1203 S M
3386 1203 L
3233 1203 S M
3233 1151 L
3233 1203 S M
3309 1203 L
3156 1203 S M
3156 1151 L
3156 1203 S M
3233 1203 L
3079 1203 S M
3079 1154 L
3079 1203 S M
3156 1203 L
3002 1203 S M
3002 1163 L
3002 1203 S M
3079 1203 L
2925 1203 S M
2925 1168 L
2925 1203 S M
3002 1203 L
2848 1203 S M
2848 1168 L
2848 1203 S M
2925 1203 L
2771 1203 S M
2771 1168 L
2771 1203 S M
2848 1203 L
2694 1175 S M
2694 1140 L
2694 1175 S M
2771 1203 L
2617 968 S M
2617 933 L
2617 968 S M
2694 1175 L
2540 890 S M
2540 855 L
2540 890 S M
2617 968 L
2463 890 S M
2463 855 L
2463 890 S M
2540 890 L
2386 968 S M
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2463 890 L
2309 1175 S M
2309 1140 L
2309 1175 S M
2386 968 L
2232 1203 S M
2232 1168 L
2232 1203 S M
2309 1175 L
2155 1203 S M
2155 1168 L
2155 1203 S M
2232 1203 L
2078 1203 S M
2078 1168 L
2078 1203 S M
2155 1203 L
2001 1175 S M
2001 1140 L
2001 1175 S M
2078 1203 L
1924 968 S M
1924 933 L
1924 968 S M
2001 1175 L
1847 890 S M
1847 854 L
1847 890 S M
1924 968 L
1770 890 S M
1770 854 L
1770 890 S M
1847 890 L
1693 968 S M
1693 933 L
1693 968 S M
1770 890 L
1616 1175 S M
1616 1140 L
1616 1175 S M
1693 968 L
1539 1202 S M
1539 1168 L
1539 1202 S M
1616 1175 L
1462 1202 S M
1462 1168 L
1462 1202 S M
1539 1202 L
1385 1202 S M
1385 1168 L
1385 1202 S M
1462 1202 L
1308 1180 S M
1308 1145 L
1308 1180 S M
1385 1202 L
1231 1018 S M
1231 986 L
1231 1018 S M
1308 1180 L
1154 973 S M
1154 945 L
1154 973 S M
1231 1018 L
1077 1018 S M
1077 986 L
1077 1018 S M
1154 973 L
1000 1180 S M
1000 1145 L
1000 1180 S M
1077 1018 L
923 1203 S M
923 1168 L
923 1203 S M
1000 1180 L
846 1203 S M
846 1168 L
846 1203 S M
923 1203 L
769 1180 S M
769 1145 L
769 1180 S M
846 1203 L
692 1018 S M
692 986 L
692 1018 S M
769 1180 L
615 973 S M
615 945 L
615 973 S M
692 1018 L
538 1018 S M
538 986 L
538 1018 S M
615 973 L
461 1180 S M
461 1145 L
461 1180 S M
538 1018 L
384 1202 S M
384 1167 L
384 1202 S M
461 1180 L
307 1202 S M
307 1167 L
307 1202 S M
384 1202 L
230 1202 S M
230 1167 L
230 1202 S M
307 1202 L
153 1100 S M
153 1065 L
153 1100 S M
230 1202 L
76 587 S M
76 552 L
76 587 S M
153 1100 L
0 520 S M
0 485 L
0 520 S M
76 587 L
5234 555 S M
5234 520 L
5157 620 S M
5157 586 L
5157 620 S M
5234 555 L
5080 1134 S M
5080 1100 L
5080 1134 S M
5157 620 L
5003 1237 S M
5003 1202 L
5003 1237 S M
5080 1134 L
4926 1237 S M
4926 1202 L
4926 1237 S M
5003 1237 L
4849 1237 S M
4849 1202 L
4849 1237 S M
4926 1237 L
4772 1237 S M
4772 1202 L
4772 1237 S M
4849 1237 L
4695 1237 S M
4695 1202 L
4695 1237 S M
4772 1237 L
4618 1237 S M
4618 1202 L
4618 1237 S M
4695 1237 L
4541 1237 S M
4541 1202 L
4541 1237 S M
4618 1237 L
4464 1237 S M
4464 1202 L
4464 1237 S M
4541 1237 L
4387 1237 S M
4387 1202 L
4387 1237 S M
4464 1237 L
4310 1237 S M
4310 1202 L
4310 1237 S M
4387 1237 L
4233 1237 S M
4233 1202 L
4233 1237 S M
4310 1237 L
4156 1237 S M
4156 1202 L
4156 1237 S M
4233 1237 L
4079 1205 S M
4079 1148 L
4079 1205 S M
4156 1237 L
4002 970 S M
4002 905 L
4002 970 S M
4079 1205 L
3925 893 S M
3925 840 L
3925 893 S M
4002 970 L
3848 899 S M
3848 853 L
3848 899 S M
3925 893 L
3771 986 S M
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3771 986 S M
3848 899 L
3694 1208 S M
3694 1173 L
3694 1208 S M
3771 986 L
3617 1237 S M
3617 1202 L
3617 1237 S M
3694 1208 L
3540 1237 S M
3540 1202 L
3540 1237 S M
3617 1237 L
3463 1237 S M
3463 1202 L
3463 1237 S M
3540 1237 L
3386 1237 S M
3386 1202 L
3386 1237 S M
3463 1237 L
3309 1237 S M
3309 1202 L
3309 1237 S M
3386 1237 L
3233 1237 S M
3233 1202 L
3233 1237 S M
3309 1237 L
3156 1237 S M
3156 1202 L
3156 1237 S M
3233 1237 L
3079 1237 S M
3079 1202 L
3079 1237 S M
3156 1237 L
3002 1237 S M
3002 1202 L
3002 1237 S M
3079 1237 L
2925 1237 S M
2925 1202 L
2925 1237 S M
3002 1237 L
2848 1237 S M
2848 1202 L
2848 1237 S M
2925 1237 L
2771 1237 S M
2771 1202 L
2771 1237 S M
2848 1237 L
2694 1210 S M
2694 1175 L
2694 1210 S M
2771 1237 L
2617 1003 S M
2617 968 L
2617 1003 S M
2694 1210 L
2540 925 S M
2540 890 L
2540 925 S M
2617 1003 L
2463 925 S M
2463 890 L
2463 925 S M
2540 925 L
2386 1003 S M
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2386 1003 S M
2463 925 L
2309 1210 S M
2309 1175 L
2309 1210 S M
2386 1003 L
2232 1237 S M
2232 1202 L
2232 1237 S M
2309 1210 L
2155 1237 S M
2155 1202 L
2155 1237 S M
2232 1237 L
2078 1237 S M
2078 1203 L
2078 1237 S M
2155 1237 L
2001 1210 S M
2001 1175 L
2001 1210 S M
2078 1237 L
1924 1003 S M
1924 968 L
1924 1003 S M
2001 1210 L
1847 925 S M
1847 890 L
1847 925 S M
1924 1003 L
1770 925 S M
1770 890 L
1770 925 S M
1847 925 L
1693 1003 S M
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1693 1003 S M
1770 925 L
1616 1210 S M
1616 1175 L
1616 1210 S M
1693 1003 L
1539 1237 S M
1539 1202 L
1539 1237 S M
1616 1210 L
1462 1237 S M
1462 1202 L
1462 1237 S M
1539 1237 L
1385 1237 S M
1385 1202 L
1385 1237 S M
1462 1237 L
1308 1214 S M
1308 1180 L
1308 1214 S M
1385 1237 L
1231 1049 S M
1231 1018 L
1231 1049 S M
1308 1214 L
1154 1004 S M
1154 973 L
1154 1004 S M
1231 1049 L
1077 1049 S M
1077 1018 L
1077 1049 S M
1154 1004 L
1000 1214 S M
1000 1180 L
1000 1214 S M
1077 1049 L
923 1237 S M
923 1202 L
923 1237 S M
1000 1214 L
846 1237 S M
846 1202 L
846 1237 S M
923 1237 L
769 1214 S M
769 1180 L
769 1214 S M
846 1237 L
692 1049 S M
692 1018 L
692 1049 S M
769 1214 L
615 1004 S M
615 973 L
615 1004 S M
692 1049 L
538 1049 S M
538 1018 L
538 1049 S M
615 1004 L
461 1214 S M
461 1180 L
461 1214 S M
538 1049 L
384 1237 S M
384 1202 L
384 1237 S M
461 1214 L
307 1237 S M
307 1202 L
307 1237 S M
384 1237 L
230 1237 S M
230 1202 L
230 1237 S M
307 1237 L
153 1135 S M
153 1100 L
153 1135 S M
230 1237 L
76 621 S M
76 587 L
76 621 S M
153 1135 L
0 555 S M
0 520 L
0 555 S M
76 621 L
5234 590 S M
5234 555 L
5157 651 S M
5157 620 L
5157 651 S M
5234 590 L
5080 1162 S M
5080 1134 L
5080 1162 S M
5157 651 L
5003 1272 S M
5003 1237 L
5003 1272 S M
5080 1162 L
4926 1272 S M
4926 1237 L
4926 1272 S M
5003 1272 L
4849 1272 S M
4849 1237 L
4849 1272 S M
4926 1272 L
4772 1272 S M
4772 1237 L
4772 1272 S M
4849 1272 L
4695 1272 S M
4695 1237 L
4695 1272 S M
4772 1272 L
4618 1272 S M
4618 1237 L
4618 1272 S M
4695 1272 L
4541 1272 S M
4541 1237 L
4541 1272 S M
4618 1272 L
4464 1272 S M
4464 1237 L
4464 1272 S M
4541 1272 L
4387 1272 S M
4387 1237 L
4387 1272 S M
4464 1272 L
4310 1272 S M
4310 1237 L
4310 1272 S M
4387 1272 L
4233 1272 S M
4233 1237 L
4233 1272 S M
4310 1272 L
4156 1272 S M
4156 1237 L
4156 1272 S M
4233 1272 L
4079 1243 S M
4079 1205 L
4079 1243 S M
4156 1272 L
4002 1019 S M
4002 970 L
4002 1019 S M
4079 1243 L
3925 940 S M
3925 893 L
3925 940 S M
4002 1019 L
3848 943 S M
3848 899 L
3848 943 S M
3925 940 L
3771 1026 S M
3771 986 L
3771 1026 S M
3848 943 L
3694 1243 S M
3694 1208 L
3694 1243 S M
3771 1026 L
3617 1272 S M
3617 1237 L
3617 1272 S M
3694 1243 L
3540 1272 S M
3540 1237 L
3540 1272 S M
3617 1272 L
3463 1272 S M
3463 1237 L
3463 1272 S M
3540 1272 L
3386 1272 S M
3386 1237 L
3386 1272 S M
3463 1272 L
3309 1272 S M
3309 1237 L
3309 1272 S M
3386 1272 L
3233 1272 S M
3233 1237 L
3233 1272 S M
3309 1272 L
3156 1272 S M
3156 1237 L
3156 1272 S M
3233 1272 L
3079 1272 S M
3079 1237 L
3079 1272 S M
3156 1272 L
3002 1272 S M
3002 1237 L
3002 1272 S M
3079 1272 L
2925 1272 S M
2925 1237 L
2925 1272 S M
3002 1272 L
2848 1272 S M
2848 1237 L
2848 1272 S M
2925 1272 L
2771 1272 S M
2771 1237 L
2771 1272 S M
2848 1272 L
2694 1245 S M
2694 1210 L
2694 1245 S M
2771 1272 L
2617 1038 S M
2617 1003 L
2617 1038 S M
2694 1245 L
2540 960 S M
2540 925 L
2540 960 S M
2617 1038 L
2463 960 S M
2463 925 L
2463 960 S M
2540 960 L
2386 1038 S M
2386 1003 L
2386 1038 S M
2463 960 L
2309 1245 S M
2309 1210 L
2309 1245 S M
2386 1038 L
2232 1272 S M
2232 1237 L
2232 1272 S M
2309 1245 L
2155 1272 S M
2155 1237 L
2155 1272 S M
2232 1272 L
2078 1272 S M
2078 1237 L
2078 1272 S M
2155 1272 L
2001 1245 S M
2001 1210 L
2001 1245 S M
2078 1272 L
1924 1038 S M
1924 1003 L
1924 1038 S M
2001 1245 L
1847 960 S M
1847 925 L
1847 960 S M
1924 1038 L
1770 960 S M
1770 925 L
1770 960 S M
1847 960 L
1693 1038 S M
1693 1003 L
1693 1038 S M
1770 960 L
1616 1245 S M
1616 1210 L
1616 1245 S M
1693 1038 L
1539 1272 S M
1539 1237 L
1539 1272 S M
1616 1245 L
1462 1272 S M
1462 1237 L
1462 1272 S M
1539 1272 L
1385 1272 S M
1385 1237 L
1385 1272 S M
1462 1272 L
1308 1248 S M
1308 1214 L
1308 1248 S M
1385 1272 L
1231 1080 S M
1231 1049 L
1231 1080 S M
1308 1248 L
1154 1033 S M
1154 1004 L
1154 1033 S M
1231 1080 L
1077 1079 S M
1077 1049 L
1077 1079 S M
1154 1033 L
1000 1248 S M
1000 1214 L
1000 1248 S M
1077 1079 L
923 1272 S M
923 1237 L
923 1272 S M
1000 1248 L
846 1272 S M
846 1237 L
846 1272 S M
923 1272 L
769 1248 S M
769 1214 L
769 1248 S M
846 1272 L
692 1079 S M
692 1049 L
692 1079 S M
769 1248 L
615 1033 S M
615 1004 L
615 1033 S M
692 1079 L
538 1080 S M
538 1049 L
538 1080 S M
615 1033 L
461 1248 S M
461 1214 L
461 1248 S M
538 1080 L
384 1272 S M
384 1237 L
384 1272 S M
461 1248 L
307 1272 S M
307 1237 L
307 1272 S M
384 1272 L
230 1272 S M
230 1237 L
230 1272 S M
307 1272 L
153 1170 S M
153 1135 L
153 1170 S M
230 1272 L
76 656 S M
76 621 L
76 656 S M
153 1170 L
0 590 S M
0 555 L
0 590 S M
76 656 L
5234 624 S M
5234 589 L
5157 677 S M
5157 651 L
5157 677 S M
5234 624 L
5080 1162 S M
5080 1162 L
5109 966 S M
5157 677 L
5003 1307 S M
5003 1272 L
5003 1307 S M
5056 1197 L
4926 1307 S M
4926 1272 L
4926 1307 S M
5003 1307 L
4849 1307 S M
4849 1272 L
4849 1307 S M
4926 1307 L
4772 1307 S M
4772 1272 L
4772 1307 S M
4849 1307 L
4695 1307 S M
4695 1272 L
4695 1307 S M
4772 1307 L
4618 1307 S M
4618 1272 L
4618 1307 S M
4695 1307 L
4541 1307 S M
4541 1272 L
4541 1307 S M
4618 1307 L
4464 1307 S M
4464 1272 L
4464 1307 S M
4541 1307 L
4387 1307 S M
4387 1272 L
4387 1307 S M
4464 1307 L
4310 1307 S M
4310 1272 L
4310 1307 S M
4387 1307 L
4233 1307 S M
4233 1272 L
4233 1307 S M
4310 1307 L
4156 1307 S M
4156 1272 L
4156 1307 S M
4233 1307 L
4079 1278 S M
4079 1242 L
4079 1278 S M
4156 1307 L
4002 1061 S M
4002 1019 L
4002 1061 S M
4079 1278 L
3925 981 S M
3925 940 L
3925 981 S M
4002 1061 L
3848 982 S M
3848 942 L
3848 982 S M
3925 981 L
3771 1064 S M
3771 1026 L
3771 1064 S M
3848 982 L
3694 1278 S M
3694 1243 L
3694 1278 S M
3771 1064 L
3617 1307 S M
3617 1272 L
3617 1307 S M
3694 1278 L
3540 1307 S M
3540 1272 L
3540 1307 S M
3617 1307 L
3463 1307 S M
3463 1272 L
3463 1307 S M
3540 1307 L
3386 1307 S M
3386 1272 L
3386 1307 S M
3463 1307 L
3309 1307 S M
3309 1272 L
3309 1307 S M
3386 1307 L
3233 1307 S M
3233 1272 L
3233 1307 S M
3309 1307 L
3156 1307 S M
3156 1272 L
3156 1307 S M
3233 1307 L
3079 1307 S M
3079 1272 L
3079 1307 S M
3156 1307 L
3002 1307 S M
3002 1272 L
3002 1307 S M
3079 1307 L
2925 1307 S M
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2925 1307 S M
3002 1307 L
2848 1307 S M
2848 1272 L
2848 1307 S M
2925 1307 L
2771 1307 S M
2771 1272 L
2771 1307 S M
2848 1307 L
2694 1279 S M
2694 1245 L
2694 1279 S M
2771 1307 L
2617 1072 S M
2617 1038 L
2617 1072 S M
2694 1279 L
2540 993 S M
2540 960 L
2540 993 S M
2617 1072 L
2463 993 S M
2463 960 L
2463 993 S M
2540 993 L
2386 1072 S M
2386 1038 L
2386 1072 S M
2463 993 L
2309 1279 S M
2309 1245 L
2309 1279 S M
2386 1072 L
2232 1307 S M
2232 1272 L
2232 1307 S M
2309 1279 L
2155 1307 S M
2155 1272 L
2155 1307 S M
2232 1307 L
2078 1307 S M
2078 1272 L
2078 1307 S M
2155 1307 L
2001 1279 S M
2001 1245 L
2001 1279 S M
2078 1307 L
1924 1072 S M
1924 1038 L
1924 1072 S M
2001 1279 L
1847 993 S M
1847 960 L
1847 993 S M
1924 1072 L
1770 993 S M
1770 960 L
1770 993 S M
1847 993 L
1693 1072 S M
1693 1038 L
1693 1072 S M
1770 993 L
1616 1279 S M
1616 1244 L
1616 1279 S M
1693 1072 L
1539 1307 S M
1539 1272 L
1539 1307 S M
1616 1279 L
1462 1307 S M
1462 1272 L
1462 1307 S M
1539 1307 L
1385 1307 S M
1385 1272 L
1385 1307 S M
1462 1307 L
1308 1283 S M
1308 1248 L
1308 1283 S M
1385 1307 L
1231 1108 S M
1231 1080 L
1231 1108 S M
1308 1283 L
1154 1058 S M
1154 1033 L
1154 1058 S M
1231 1108 L
1077 1106 S M
1077 1079 L
1077 1106 S M
1154 1058 L
1000 1282 S M
1000 1248 L
1000 1282 S M
1077 1106 L
923 1307 S M
923 1272 L
923 1307 S M
1000 1282 L
846 1307 S M
846 1272 L
846 1307 S M
923 1307 L
769 1282 S M
769 1248 L
769 1282 S M
846 1307 L
692 1106 S M
692 1079 L
692 1106 S M
769 1282 L
615 1058 S M
615 1033 L
615 1058 S M
692 1106 L
538 1108 S M
538 1080 L
538 1108 S M
615 1058 L
461 1282 S M
461 1248 L
461 1282 S M
538 1108 L
384 1306 S M
384 1272 L
384 1306 S M
461 1282 L
307 1306 S M
307 1272 L
307 1306 S M
384 1306 L
230 1306 S M
230 1272 L
230 1306 S M
307 1306 L
153 1204 S M
153 1170 L
153 1204 S M
230 1306 L
76 691 S M
76 656 L
76 691 S M
153 1204 L
0 624 S M
0 589 L
0 624 S M
76 691 L
5234 659 S M
5234 624 L
5157 694 S M
5157 677 L
5157 694 S M
5234 659 L
5153 703 S M
5157 694 L
5003 1307 S M
5003 1307 L
4926 1307 S M
4926 1307 L
4849 1313 S M
4849 1307 L
4849 1313 S M
4902 1307 L
4772 1317 S M
4772 1307 L
4772 1317 S M
4849 1313 L
4695 1319 S M
4695 1307 L
4695 1319 S M
4772 1317 L
4618 1321 S M
4618 1307 L
4618 1321 S M
4695 1319 L
4541 1324 S M
4541 1307 L
4541 1324 S M
4618 1321 L
4464 1328 S M
4464 1307 L
4464 1328 S M
4541 1324 L
4387 1337 S M
4387 1307 L
4387 1337 S M
4464 1328 L
4310 1341 S M
4310 1307 L
4310 1341 S M
4387 1337 L
4233 1341 S M
4233 1307 L
4233 1341 S M
4310 1341 L
4156 1341 S M
4156 1307 L
4156 1341 S M
4233 1341 L
4079 1313 S M
4079 1278 L
4079 1313 S M
4156 1341 L
4002 1099 S M
4002 1061 L
4002 1099 S M
4079 1313 L
3925 1019 S M
3925 981 L
3925 1019 S M
4002 1099 L
3848 1019 S M
3848 982 L
3848 1019 S M
3925 1019 L
3771 1100 S M
3771 1064 L
3771 1100 S M
3848 1019 L
3694 1313 S M
3694 1278 L
3694 1313 S M
3771 1100 L
3617 1341 S M
3617 1307 L
3617 1341 S M
3694 1313 L
3540 1341 S M
3540 1307 L
3540 1341 S M
3617 1341 L
3463 1341 S M
3463 1307 L
3463 1341 S M
3540 1341 L
3386 1337 S M
3386 1307 L
3386 1337 S M
3463 1341 L
3309 1329 S M
3309 1307 L
3309 1329 S M
3386 1337 L
3233 1326 S M
3233 1307 L
3233 1326 S M
3309 1329 L
3156 1326 S M
3156 1307 L
3156 1326 S M
3233 1326 L
3079 1329 S M
3079 1307 L
3079 1329 S M
3156 1326 L
3002 1337 S M
3002 1307 L
3002 1337 S M
3079 1329 L
2925 1341 S M
2925 1307 L
2925 1341 S M
3002 1337 L
2848 1341 S M
2848 1307 L
2848 1341 S M
2925 1341 L
2771 1341 S M
2771 1307 L
2771 1341 S M
2848 1341 L
2694 1314 S M
2694 1279 L
2694 1314 S M
2771 1341 L
2617 1105 S M
2617 1072 L
2617 1105 S M
2694 1314 L
2540 1026 S M
2540 993 L
2540 1026 S M
2617 1105 L
2463 1026 S M
2463 993 L
2463 1026 S M
2540 1026 L
2386 1105 S M
2386 1072 L
2386 1105 S M
2463 1026 L
2309 1314 S M
2309 1279 L
2309 1314 S M
2386 1105 L
2232 1341 S M
2232 1307 L
2232 1341 S M
2309 1314 L
2155 1341 S M
2155 1307 L
2155 1341 S M
2232 1341 L
2078 1341 S M
2078 1307 L
2078 1341 S M
2155 1341 L
2001 1314 S M
2001 1279 L
2001 1314 S M
2078 1341 L
1924 1105 S M
1924 1072 L
1924 1105 S M
2001 1314 L
1847 1026 S M
1847 993 L
1847 1026 S M
1924 1105 L
1770 1026 S M
1770 993 L
1770 1026 S M
1847 1026 L
1693 1105 S M
1693 1072 L
1693 1105 S M
1770 1026 L
1616 1314 S M
1616 1279 L
1616 1314 S M
1693 1105 L
1539 1341 S M
1539 1306 L
1539 1341 S M
1616 1314 L
1462 1341 S M
1462 1306 L
1462 1341 S M
1539 1341 L
1385 1341 S M
1385 1306 L
1385 1341 S M
1462 1341 L
1308 1316 S M
1308 1282 L
1308 1316 S M
1385 1341 L
1231 1132 S M
1231 1108 L
1231 1132 S M
1308 1316 L
1154 1078 S M
1154 1058 L
1154 1078 S M
1231 1132 L
1077 1125 S M
1077 1105 L
1077 1125 S M
1154 1078 L
1000 1315 S M
1000 1282 L
1000 1315 S M
1077 1125 L
923 1341 S M
923 1307 L
923 1341 S M
1000 1315 L
846 1341 S M
846 1307 L
846 1341 S M
923 1341 L
769 1315 S M
769 1282 L
769 1315 S M
846 1341 L
692 1125 S M
692 1105 L
692 1125 S M
769 1315 L
615 1077 S M
615 1058 L
615 1077 S M
692 1125 L
538 1131 S M
538 1108 L
538 1131 S M
615 1077 L
461 1316 S M
461 1282 L
461 1316 S M
538 1131 L
384 1341 S M
384 1306 L
384 1341 S M
461 1316 L
307 1341 S M
307 1306 L
307 1341 S M
384 1341 L
230 1341 S M
230 1306 L
230 1341 S M
307 1341 L
153 1239 S M
153 1204 L
153 1239 S M
230 1341 L
76 726 S M
76 691 L
76 726 S M
153 1239 L
0 659 S M
0 624 L
0 659 S M
76 726 L
5234 694 S M
5234 659 L
5157 718 S M
5157 694 L
5157 718 S M
5234 694 L
5150 725 S M
5157 718 L
4849 1313 S M
4849 1313 L
4772 1317 S M
4772 1317 L
4695 1319 S M
4695 1319 L
4618 1321 S M
4618 1321 L
4541 1324 S M
4541 1324 L
4464 1328 S M
4464 1328 L
4387 1360 S M
4387 1337 L
4387 1360 S M
4407 1335 L
4310 1376 S M
4310 1341 L
4310 1376 S M
4387 1360 L
4233 1376 S M
4233 1341 L
4233 1376 S M
4310 1376 L
4156 1376 S M
4156 1341 L
4156 1376 S M
4233 1376 L
4079 1348 S M
4079 1313 L
4079 1348 S M
4156 1376 L
4002 1134 S M
4002 1099 L
4002 1134 S M
4079 1348 L
3925 1053 S M
3925 1019 L
3925 1053 S M
4002 1134 L
3848 1053 S M
3848 1019 L
3848 1053 S M
3925 1053 L
3771 1134 S M
3771 1100 L
3771 1134 S M
3848 1053 L
3694 1348 S M
3694 1313 L
3694 1348 S M
3771 1134 L
3617 1376 S M
3617 1341 L
3617 1376 S M
3694 1348 L
3540 1376 S M
3540 1341 L
3540 1376 S M
3617 1376 L
3463 1376 S M
3463 1341 L
3463 1376 S M
3540 1376 L
3386 1361 S M
3386 1337 L
3386 1361 S M
3463 1376 L
3309 1329 S M
3309 1329 L
3362 1335 S M
3386 1361 L
3233 1326 S M
3233 1326 L
3156 1326 S M
3156 1326 L
3079 1329 S M
3079 1329 L
3002 1361 S M
3002 1337 L
3002 1361 S M
3026 1335 L
2925 1376 S M
2925 1341 L
2925 1376 S M
3002 1361 L
2848 1376 S M
2848 1341 L
2848 1376 S M
2925 1376 L
2771 1376 S M
2771 1341 L
2771 1376 S M
2848 1376 L
2694 1348 S M
2694 1314 L
2694 1348 S M
2771 1376 L
2617 1137 S M
2617 1105 L
2617 1137 S M
2694 1348 L
2540 1058 S M
2540 1026 L
2540 1058 S M
2617 1137 L
2463 1058 S M
2463 1026 L
2463 1058 S M
2540 1058 L
2386 1137 S M
2386 1105 L
2386 1137 S M
2463 1058 L
2309 1348 S M
2309 1314 L
2309 1348 S M
2386 1137 L
2232 1376 S M
2232 1341 L
2232 1376 S M
2309 1348 L
2155 1376 S M
2155 1341 L
2155 1376 S M
2232 1376 L
2078 1376 S M
2078 1341 L
2078 1376 S M
2155 1376 L
2001 1348 S M
2001 1314 L
2001 1348 S M
2078 1376 L
1924 1137 S M
1924 1105 L
1924 1137 S M
2001 1348 L
1847 1058 S M
1847 1026 L
1847 1058 S M
1924 1137 L
1770 1058 S M
1770 1026 L
1770 1058 S M
1847 1058 L
1693 1137 S M
1693 1105 L
1693 1137 S M
1770 1058 L
1616 1348 S M
1616 1314 L
1616 1348 S M
1693 1137 L
1539 1376 S M
1539 1341 L
1539 1376 S M
1616 1348 L
1462 1376 S M
1462 1341 L
1462 1376 S M
1539 1376 L
1385 1376 S M
1385 1341 L
1385 1376 S M
1462 1376 L
1308 1349 S M
1308 1316 L
1308 1349 S M
1385 1376 L
1231 1149 S M
1231 1131 L
1231 1149 S M
1308 1349 L
1154 1087 S M
1154 1077 L
1154 1087 S M
1231 1149 L
1077 1131 S M
1077 1125 L
1077 1131 S M
1154 1087 L
1000 1345 S M
1000 1315 L
1000 1345 S M
1077 1131 L
923 1376 S M
923 1341 L
923 1376 S M
1000 1345 L
846 1376 S M
846 1341 L
846 1376 S M
923 1376 L
769 1345 S M
769 1315 L
769 1345 S M
846 1376 L
692 1131 S M
692 1125 L
692 1131 S M
769 1345 L
615 1087 S M
615 1077 L
615 1087 S M
692 1131 L
538 1149 S M
538 1131 L
538 1149 S M
615 1087 L
461 1349 S M
461 1316 L
461 1349 S M
538 1149 L
384 1376 S M
384 1341 L
384 1376 S M
461 1349 L
307 1376 S M
307 1341 L
307 1376 S M
384 1376 L
230 1376 S M
230 1341 L
230 1376 S M
307 1376 L
153 1274 S M
153 1239 L
153 1274 S M
230 1376 L
76 760 S M
76 725 L
76 760 S M
153 1274 L
0 694 S M
0 659 L
0 694 S M
76 760 L
5234 728 S M
5234 694 L
5157 747 S M
5157 718 L
5157 747 S M
5234 728 L
5144 754 S M
5157 747 L
4387 1391 S M
4387 1360 L
4387 1391 S M
4419 1334 L
4310 1411 S M
4310 1376 L
4310 1411 S M
4387 1391 L
4233 1411 S M
4233 1376 L
4233 1411 S M
4310 1411 L
4156 1411 S M
4156 1376 L
4156 1411 S M
4233 1411 L
4079 1382 S M
4079 1348 L
4079 1382 S M
4156 1411 L
4002 1166 S M
4002 1134 L
4002 1166 S M
4079 1382 L
3925 1084 S M
3925 1053 L
3925 1084 S M
4002 1166 L
3848 1084 S M
3848 1053 L
3848 1084 S M
3925 1084 L
3771 1166 S M
3771 1134 L
3771 1166 S M
3848 1084 L
3694 1382 S M
3694 1348 L
3694 1382 S M
3771 1166 L
3617 1411 S M
3617 1376 L
3617 1411 S M
3694 1382 L
3540 1411 S M
3540 1376 L
3540 1411 S M
3617 1411 L
3463 1411 S M
3463 1376 L
3463 1411 S M
3540 1411 L
3386 1392 S M
3386 1361 L
3386 1392 S M
3463 1411 L
3349 1334 S M
3386 1392 L
3002 1392 S M
3002 1361 L
3002 1392 S M
3040 1334 L
2925 1411 S M
2925 1376 L
2925 1411 S M
3002 1392 L
2848 1411 S M
2848 1376 L
2848 1411 S M
2925 1411 L
2771 1411 S M
2771 1376 L
2771 1411 S M
2848 1411 L
2694 1383 S M
2694 1348 L
2694 1383 S M
2771 1411 L
2617 1168 S M
2617 1137 L
2617 1168 S M
2694 1383 L
2540 1087 S M
2540 1058 L
2540 1087 S M
2617 1168 L
2463 1087 S M
2463 1058 L
2463 1087 S M
2540 1087 L
2386 1168 S M
2386 1137 L
2386 1168 S M
2463 1087 L
2309 1383 S M
2309 1348 L
2309 1383 S M
2386 1168 L
2232 1411 S M
2232 1376 L
2232 1411 S M
2309 1383 L
2155 1411 S M
2155 1376 L
2155 1411 S M
2232 1411 L
2078 1411 S M
2078 1376 L
2078 1411 S M
2155 1411 L
2001 1383 S M
2001 1348 L
2001 1383 S M
2078 1411 L
1924 1168 S M
1924 1137 L
1924 1168 S M
2001 1383 L
1847 1087 S M
1847 1058 L
1847 1087 S M
1924 1168 L
1770 1087 S M
1770 1058 L
1770 1087 S M
1847 1087 L
1693 1168 S M
1693 1137 L
1693 1168 S M
1770 1087 L
1616 1382 S M
1616 1348 L
1616 1382 S M
1693 1168 L
1539 1411 S M
1539 1376 L
1539 1411 S M
1616 1382 L
1462 1411 S M
1462 1376 L
1462 1411 S M
1539 1411 L
1385 1411 S M
1385 1376 L
1385 1411 S M
1462 1411 L
1308 1381 S M
1308 1349 L
1308 1381 S M
1385 1411 L
1231 1158 S M
1231 1149 L
1231 1158 S M
1308 1381 L
1154 1087 S M
1154 1086 L
1182 1109 S M
1231 1158 L
1077 1131 S M
1077 1131 L
1000 1348 S M
1000 1345 L
1000 1348 S M
1010 1318 L
923 1411 S M
923 1376 L
923 1411 S M
1000 1348 L
846 1411 S M
846 1376 L
846 1411 S M
923 1411 L
769 1348 S M
769 1345 L
769 1348 S M
846 1411 L
692 1131 S M
692 1131 L
760 1318 S M
769 1348 L
615 1087 S M
615 1086 L
538 1158 S M
538 1149 L
538 1158 S M
588 1109 L
461 1381 S M
461 1349 L
461 1381 S M
538 1158 L
384 1411 S M
384 1376 L
384 1411 S M
461 1381 L
307 1411 S M
307 1376 L
307 1411 S M
384 1411 L
230 1411 S M
230 1376 L
230 1411 S M
307 1411 L
153 1308 S M
153 1274 L
153 1308 S M
230 1411 L
76 795 S M
76 760 L
76 795 S M
153 1308 L
0 728 S M
0 694 L
0 728 S M
76 795 L
5234 763 S M
5234 728 L
5157 780 S M
5157 747 L
5157 780 S M
5234 763 L
5139 789 S M
5157 780 L
4387 1424 S M
4387 1391 L
4387 1424 S M
4434 1333 L
4310 1445 S M
4310 1411 L
4310 1445 S M
4387 1424 L
4233 1445 S M
4233 1411 L
4233 1445 S M
4310 1445 L
4156 1445 S M
4156 1411 L
4156 1445 S M
4233 1445 L
4079 1416 S M
4079 1382 L
4079 1416 S M
4156 1445 L
4002 1195 S M
4002 1166 L
4002 1195 S M
4079 1416 L
3925 1112 S M
3925 1084 L
3925 1112 S M
4002 1195 L
3848 1112 S M
3848 1084 L
3848 1112 S M
3925 1112 L
3771 1195 S M
3771 1166 L
3771 1195 S M
3848 1112 L
3694 1416 S M
3694 1382 L
3694 1416 S M
3771 1195 L
3617 1445 S M
3617 1411 L
3617 1445 S M
3694 1416 L
3540 1445 S M
3540 1411 L
3540 1445 S M
3617 1445 L
3463 1445 S M
3463 1411 L
3463 1445 S M
3540 1445 L
3386 1426 S M
3386 1392 L
3386 1426 S M
3463 1445 L
3331 1332 S M
3386 1426 L
3002 1426 S M
3002 1392 L
3002 1426 S M
3057 1332 L
2925 1445 S M
2925 1411 L
2925 1445 S M
3002 1426 L
2848 1445 S M
2848 1411 L
2848 1445 S M
2925 1445 L
2771 1445 S M
2771 1411 L
2771 1445 S M
2848 1445 L
2694 1417 S M
2694 1382 L
2694 1417 S M
2771 1445 L
2617 1196 S M
2617 1168 L
2617 1196 S M
2694 1417 L
2540 1113 S M
2540 1087 L
2540 1113 S M
2617 1196 L
2463 1113 S M
2463 1087 L
2463 1113 S M
2540 1113 L
2386 1196 S M
2386 1168 L
2386 1196 S M
2463 1113 L
2309 1417 S M
2309 1383 L
2309 1417 S M
2386 1196 L
2232 1446 S M
2232 1411 L
2232 1446 S M
2309 1417 L
2155 1446 S M
2155 1411 L
2155 1446 S M
2232 1446 L
2078 1446 S M
2078 1411 L
2078 1446 S M
2155 1446 L
2001 1417 S M
2001 1383 L
2001 1417 S M
2078 1446 L
1924 1196 S M
1924 1168 L
1924 1196 S M
2001 1417 L
1847 1113 S M
1847 1087 L
1847 1113 S M
1924 1196 L
1770 1113 S M
1770 1087 L
1770 1113 S M
1847 1113 L
1693 1196 S M
1693 1168 L
1693 1196 S M
1770 1113 L
1616 1416 S M
1616 1382 L
1616 1416 S M
1693 1196 L
1539 1445 S M
1539 1411 L
1539 1445 S M
1616 1416 L
1462 1445 S M
1462 1411 L
1462 1445 S M
1539 1445 L
1385 1445 S M
1385 1411 L
1385 1445 S M
1462 1445 L
1308 1413 S M
1308 1381 L
1308 1413 S M
1385 1445 L
1231 1159 S M
1231 1158 L
1231 1159 S M
1308 1413 L
1228 1155 S M
1231 1159 L
1000 1348 S M
1000 1347 L
923 1411 S M
923 1411 L
846 1411 S M
846 1411 L
769 1348 S M
769 1347 L
538 1159 S M
538 1158 L
538 1159 S M
541 1155 L
461 1412 S M
461 1381 L
461 1412 S M
538 1159 L
384 1445 S M
384 1410 L
384 1445 S M
461 1412 L
307 1445 S M
307 1410 L
307 1445 S M
384 1445 L
230 1445 S M
230 1410 L
230 1445 S M
307 1445 L
153 1343 S M
153 1308 L
153 1343 S M
230 1445 L
76 830 S M
76 795 L
76 830 S M
153 1343 L
0 763 S M
0 728 L
0 763 S M
76 830 L
5234 798 S M
5234 763 L
5157 816 S M
5157 780 L
5157 816 S M
5234 798 L
5132 831 S M
5157 816 L
4387 1460 S M
4387 1424 L
4387 1460 S M
4460 1329 L
4310 1480 S M
4310 1445 L
4310 1480 S M
4387 1460 L
4233 1480 S M
4233 1445 L
4233 1480 S M
4310 1480 L
4156 1480 S M
4156 1445 L
4156 1480 S M
4233 1480 L
4079 1450 S M
4079 1416 L
4079 1450 S M
4156 1480 L
4002 1219 S M
4002 1195 L
4002 1219 S M
4079 1450 L
3925 1134 S M
3925 1112 L
3925 1134 S M
4002 1219 L
3848 1134 S M
3848 1112 L
3848 1134 S M
3925 1134 L
3771 1219 S M
3771 1195 L
3771 1219 S M
3848 1134 L
3694 1450 S M
3694 1416 L
3694 1450 S M
3771 1219 L
3617 1480 S M
3617 1445 L
3617 1480 S M
3694 1450 L
3540 1480 S M
3540 1445 L
3540 1480 S M
3617 1480 L
3463 1480 S M
3463 1445 L
3463 1480 S M
3540 1480 L
3386 1462 S M
3386 1426 L
3386 1462 S M
3463 1480 L
3309 1343 S M
3309 1329 L
3309 1343 S M
3386 1462 L
3284 1328 S M
3309 1343 L
3079 1343 S M
3079 1329 L
3079 1343 S M
3104 1328 L
3002 1462 S M
3002 1426 L
3002 1462 S M
3079 1343 L
2925 1480 S M
2925 1445 L
2925 1480 S M
3002 1462 L
2848 1480 S M
2848 1445 L
2848 1480 S M
2925 1480 L
2771 1480 S M
2771 1445 L
2771 1480 S M
2848 1480 L
2694 1450 S M
2694 1417 L
2694 1450 S M
2771 1480 L
2617 1220 S M
2617 1196 L
2617 1220 S M
2694 1450 L
2540 1135 S M
2540 1113 L
2540 1135 S M
2617 1220 L
2463 1135 S M
2463 1113 L
2463 1135 S M
2540 1135 L
2386 1220 S M
2386 1196 L
2386 1220 S M
2463 1135 L
2309 1450 S M
2309 1417 L
2309 1450 S M
2386 1220 L
2232 1480 S M
2232 1445 L
2232 1480 S M
2309 1450 L
2155 1480 S M
2155 1445 L
2155 1480 S M
2232 1480 L
2078 1480 S M
2078 1445 L
2078 1480 S M
2155 1480 L
2001 1450 S M
2001 1417 L
2001 1450 S M
2078 1480 L
1924 1220 S M
1924 1196 L
1924 1220 S M
2001 1450 L
1847 1135 S M
1847 1113 L
1847 1135 S M
1924 1220 L
1770 1135 S M
1770 1113 L
1770 1135 S M
1847 1135 L
1693 1220 S M
1693 1196 L
1693 1220 S M
1770 1135 L
1616 1450 S M
1616 1416 L
1616 1450 S M
1693 1220 L
1539 1480 S M
1539 1445 L
1539 1480 S M
1616 1450 L
1462 1480 S M
1462 1445 L
1462 1480 S M
1539 1480 L
1385 1480 S M
1385 1445 L
1385 1480 S M
1462 1480 L
1308 1443 S M
1308 1412 L
1308 1443 S M
1385 1480 L
1231 1159 S M
1231 1159 L
1240 1187 S M
1308 1443 L
538 1159 S M
538 1159 L
461 1443 S M
461 1412 L
461 1443 S M
530 1187 L
384 1480 S M
384 1445 L
384 1480 S M
461 1443 L
307 1480 S M
307 1445 L
307 1480 S M
384 1480 L
230 1480 S M
230 1445 L
230 1480 S M
307 1480 L
153 1378 S M
153 1343 L
153 1378 S M
230 1480 L
76 864 S M
76 830 L
76 864 S M
153 1378 L
0 798 S M
0 763 L
0 798 S M
76 864 L
5234 833 S M
5234 798 L
5157 856 S M
5157 816 L
5157 856 S M
5234 833 L
5123 888 S M
5157 856 L
4618 1329 S M
4618 1321 L
4618 1329 S M
4646 1321 L
4541 1356 S M
4541 1324 L
4541 1356 S M
4618 1329 L
4464 1402 S M
4464 1328 L
4464 1402 S M
4541 1356 L
4387 1499 S M
4387 1460 L
4387 1499 S M
4464 1402 L
4310 1515 S M
4310 1480 L
4310 1515 S M
4387 1499 L
4233 1515 S M
4233 1480 L
4233 1515 S M
4310 1515 L
4156 1515 S M
4156 1480 L
4156 1515 S M
4233 1515 L
4079 1483 S M
4079 1450 L
4079 1483 S M
4156 1515 L
4002 1238 S M
4002 1219 L
4002 1238 S M
4079 1483 L
3925 1148 S M
3925 1134 L
3925 1148 S M
4002 1238 L
3848 1148 S M
3848 1134 L
3848 1148 S M
3925 1148 L
3771 1238 S M
3771 1219 L
3771 1238 S M
3848 1148 L
3694 1483 S M
3694 1450 L
3694 1483 S M
3771 1238 L
3617 1515 S M
3617 1480 L
3617 1515 S M
3694 1483 L
3540 1515 S M
3540 1480 L
3540 1515 S M
3617 1515 L
3463 1515 S M
3463 1480 L
3463 1515 S M
3540 1515 L
3386 1500 S M
3386 1462 L
3386 1500 S M
3463 1515 L
3309 1416 S M
3309 1343 L
3309 1416 S M
3386 1500 L
3233 1386 S M
3233 1326 L
3233 1386 S M
3309 1416 L
3156 1386 S M
3156 1326 L
3156 1386 S M
3233 1386 L
3079 1416 S M
3079 1343 L
3079 1416 S M
3156 1386 L
3002 1500 S M
3002 1462 L
3002 1500 S M
3079 1416 L
2925 1515 S M
2925 1480 L
2925 1515 S M
3002 1500 L
2848 1515 S M
2848 1480 L
2848 1515 S M
2925 1515 L
2771 1515 S M
2771 1480 L
2771 1515 S M
2848 1515 L
2694 1483 S M
2694 1450 L
2694 1483 S M
2771 1515 L
2617 1238 S M
2617 1220 L
2617 1238 S M
2694 1483 L
2540 1149 S M
2540 1135 L
2540 1149 S M
2617 1238 L
2463 1149 S M
2463 1135 L
2463 1149 S M
2540 1149 L
2386 1238 S M
2386 1220 L
2386 1238 S M
2463 1149 L
2309 1483 S M
2309 1450 L
2309 1483 S M
2386 1238 L
2232 1515 S M
2232 1480 L
2232 1515 S M
2309 1483 L
2155 1515 S M
2155 1480 L
2155 1515 S M
2232 1515 L
2078 1515 S M
2078 1480 L
2078 1515 S M
2155 1515 L
2001 1483 S M
2001 1450 L
2001 1483 S M
2078 1515 L
1924 1238 S M
1924 1220 L
1924 1238 S M
2001 1483 L
1847 1149 S M
1847 1135 L
1847 1149 S M
1924 1238 L
1770 1149 S M
1770 1135 L
1770 1149 S M
1847 1149 L
1693 1238 S M
1693 1220 L
1693 1238 S M
1770 1149 L
1616 1483 S M
1616 1450 L
1616 1483 S M
1693 1238 L
1539 1515 S M
1539 1480 L
1539 1515 S M
1616 1483 L
1462 1515 S M
1462 1480 L
1462 1515 S M
1539 1515 L
1385 1515 S M
1385 1480 L
1385 1515 S M
1462 1515 L
1308 1473 S M
1308 1443 L
1308 1473 S M
1385 1515 L
1242 1195 S M
1308 1473 L
461 1472 S M
461 1443 L
461 1472 S M
528 1195 L
384 1515 S M
384 1480 L
384 1515 S M
461 1472 L
307 1515 S M
307 1480 L
307 1515 S M
384 1515 L
230 1515 S M
230 1480 L
230 1515 S M
307 1515 L
153 1412 S M
153 1378 L
153 1412 S M
230 1515 L
76 899 S M
76 864 L
76 899 S M
153 1412 L
0 833 S M
0 798 L
0 833 S M
76 899 L
5234 867 S M
5234 832 L
5157 902 S M
5157 856 L
5157 902 S M
5234 867 L
5103 1010 S M
5157 902 L
5003 1469 S M
5003 1307 L
5003 1469 S M
5053 1204 L
4926 1512 S M
4926 1307 L
4926 1512 S M
5003 1469 L
4849 1521 S M
4849 1313 L
4849 1521 S M
4926 1512 L
4772 1525 S M
4772 1317 L
4772 1525 S M
4849 1521 L
4695 1527 S M
4695 1319 L
4695 1527 S M
4772 1525 L
4618 1529 S M
4618 1329 L
4618 1529 S M
4695 1527 L
4541 1532 S M
4541 1356 L
4541 1532 S M
4618 1529 L
4464 1536 S M
4464 1402 L
4464 1536 S M
4541 1532 L
4387 1545 S M
4387 1499 L
4387 1545 S M
4464 1536 L
4310 1550 S M
4310 1515 L
4310 1550 S M
4387 1545 L
4233 1550 S M
4233 1515 L
4233 1550 S M
4310 1550 L
4156 1550 S M
4156 1515 L
4156 1550 S M
4233 1550 L
4079 1515 S M
4079 1483 L
4079 1515 S M
4156 1550 L
4002 1247 S M
4002 1238 L
4002 1247 S M
4079 1515 L
3925 1152 S M
3925 1148 L
3925 1152 S M
4002 1247 L
3848 1152 S M
3848 1148 L
3848 1152 S M
3925 1152 L
3771 1247 S M
3771 1238 L
3771 1247 S M
3848 1152 L
3694 1515 S M
3694 1483 L
3694 1515 S M
3771 1247 L
3617 1550 S M
3617 1515 L
3617 1550 S M
3694 1515 L
3540 1550 S M
3540 1515 L
3540 1550 S M
3617 1550 L
3463 1550 S M
3463 1515 L
3463 1550 S M
3540 1550 L
3386 1545 S M
3386 1500 L
3386 1545 S M
3463 1550 L
3309 1537 S M
3309 1416 L
3309 1537 S M
3386 1545 L
3233 1535 S M
3233 1386 L
3233 1535 S M
3309 1537 L
3156 1535 S M
3156 1386 L
3156 1535 S M
3233 1535 L
3079 1537 S M
3079 1416 L
3079 1537 S M
3156 1535 L
3002 1545 S M
3002 1500 L
3002 1545 S M
3079 1537 L
2925 1550 S M
2925 1515 L
2925 1550 S M
3002 1545 L
2848 1550 S M
2848 1515 L
2848 1550 S M
2925 1550 L
2771 1550 S M
2771 1515 L
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%%EOF


%%EndDocument
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(whic)m(h)120 672 y(is)39 b(the)g(union)g(of)f(a)g(\014nite)h(set)g(of)
f(op)s(en)g(arc)h(pieces)h(suc)m(h)g(that)e(no)h(comp)s(onen)m(t)g(of)f
Fn(@)5 b FA(\012)27 b Fl(n)f FA(\000)3603 687 y Fm(k)120
816 y FA(consists)34 b(only)f(of)f(a)h(single)g(p)s(oin)m(t.)120
1069 y(This)g(class)h(of)d(domains)i(\012)g(and)f(parts)h(\000)1669
1084 y Fm(k)1743 1069 y FA(of)f(its)h(b)s(oundary)f Fn(@)5
b FA(\012)34 b(to)e(b)s(e)g(con)m(tacted)i(from)d(the)120
1213 y(outside)f(co)m(v)m(ers)h(almost)e(all)g(spatially)h(t)m(w)m(o)g
(dimensional)g(problems)g(encoun)m(tered)i(in)d(science)120
1358 y(and)k(engineering.)120 1562 y Fr(2.2)47 b(Remark.)f
FA(Assumption)d(2.1)d(implies)i(the)f(follo)m(wing)g(condition)g(on)g
(\012)g(and)g(the)g(sets)120 1707 y(\000)181 1722 y Fm(k)224
1707 y FA(:)70 b(F)-8 b(or)45 b(ev)m(ery)j(p)s(oin)m(t)e
Fn(x)52 b Fl(2)f Fn(@)5 b FA(\012)47 b(there)g(exist)g(an)f(op)s(en)g
(neigh)m(b)s(ourho)s(o)s(d)g Fl(U)61 b(\032)51 b Fj(R)3353
1671 y Fk(2)3439 1707 y FA(of)45 b Fn(x)p FA(,)120 1851
y(another)29 b(op)s(en)g(set)h Fl(O)g(\032)e Fj(R)1141
1815 y Fk(2)1181 1851 y FA(,)h(and)g(a)g(bi{Lipsc)m(hitz)i
(transformation)d Fl(L)h FA(from)g Fl(U)39 b FA(on)m(to)28
b Fl(O)k FA(with)120 1996 y(almost)g(ev)m(erywhere)i(constan)m(t)e
(absolute)g(v)-5 b(alue)32 b(of)f(the)h(functional)f(determinan)m(t)i
(suc)m(h)g(that)120 2140 y Fl(L)189 2060 y Fi(\000)234
2140 y Fl(U)h(\\)23 b FA(\(\012)h Fl([)f FA(\000)701
2155 y Fm(k)744 2140 y FA(\))782 2060 y Fi(\001)861 2140
y FA(coincides)36 b(either)f(with)f(the)h(op)s(en)f(unit)g(half)g(ball)
g(in)g Fn(R)2965 2104 y Fk(2)3005 2140 y FA(,)g(the)g(op)s(en)h(unit)
120 2285 y(half)c(ball)g(united)g(with)h(its)f(ground)g(plate,)h(or)e
(the)i(op)s(en)f(unit)g(half)f(ball)h(united)h(with)g(half)e(of)120
2429 y(its)k(ground)f(plate,)h(cf.)45 b([18,)33 b(Ch.)h(I)f(Thm.)h
(2.5].)45 b(These)35 b(three)f(mo)s(del)g(sets)g(ma)m(y)g(b)s(e)g
(replaced)120 2574 y(b)m(y)28 b(just)g(t)m(w)m(o)g(mo)s(del)f(sets,)j
(namely)e(the)g(op)s(en)f(unit)h(ball)f(and)g(the)h(op)s(en)f(unit)h
(half)f(ball)g(united)120 2718 y(with)35 b(its)f(ground)h(plate,)f(cf.)
49 b([6].)f(Th)m(us)36 b(Assumption)f(2.1)f(implies)i(for)e(eac)m(h)h
Fn(k)e Fl(2)e(f)p FA(1)p Fn(;)17 b(:)g(:)g(:)e(;)i(l)r
Fl(g)120 2863 y FA(the)33 b(regularit)m(y)g(of)f(the)h(set)h(\012)22
b Fl([)h FA(\000)1406 2878 y Fm(k)1481 2863 y FA(in)33
b(the)g(sense)h(of)e Fs(Gr)2273 2859 y(\177)2269 2863
y(oger)p FA(,)h(cf.)43 b([8],)33 b([9].)120 3115 y(If)47
b Fn(p)g FA(is)h(from)e([1)p Fn(;)17 b Fl(1)p FA([,)50
b(then)e(w)m(e)g(denote)g(the)g(space)g(of)e(real,)51
b(Leb)s(esgue)e(measurable,)j(p{)120 3259 y(in)m(tegrable)38
b(functions)g(on)f(\012)h(b)m(y)g Fn(L)1456 3223 y Fm(p)1496
3259 y FA(.)57 b(Moreo)m(v)m(er,)40 b(w)m(e)f(denote)f(the)f(space)i
(of)d(real)i(Leb)s(esgue)120 3404 y(measurable,)45 b(essen)m(tially)f
(b)s(ounded)f(functions)f(on)g(\012)g(b)m(y)g Fn(L)2448
3368 y Fh(1)2523 3404 y FA(.)71 b(By)42 b Fr(L)2850 3368
y Fm(p)2933 3404 y FA(=)g Fn(L)3117 3368 y Fm(p)3186
3404 y Fl(\002)28 b Fn(:)17 b(:)g(:)28 b Fl(\002)h Fn(L)3606
3368 y Fm(p)120 3548 y FA(w)m(e)45 b(denote)f(the)g Fn(l)h
FA(times)g(direct)f(pro)s(duct)g(of)f(the)h(spaces)h
Fn(L)2466 3512 y Fm(p)2506 3548 y FA(,)i Fn(p)f Fl(2)h
FA([1)p Fn(;)17 b Fl(1)p FA(].)75 b(If)44 b Fn(s)i Fl(2)h
FA([0)p Fn(;)17 b FA(1])120 3693 y(and)33 b Fn(q)g Fl(2)p
FA(]1)p Fn(;)17 b Fl(1)p FA([,)34 b(then)f(w)m(e)i(denote|as)f(usual,)g
(cf.)46 b([17]|b)m(y)34 b Fn(H)2531 3656 y Fm(s;q)2654
3693 y FA(the)f(space)i(of)e(real)g(Bessel)120 3837 y(p)s(oten)m(tials)
f(with)h(the)f(di\013eren)m(tiabilit)m(y)i(index)f Fn(s)e
FA(and)h(the)g(in)m(tegrabilit)m(y)h(index)g Fn(q)j FA(on)31
b(the)h(set)120 3982 y(\012.)42 b(N.B.)28 b(for)f Fn(s)h
FA(=)f(1)g(these)i(spaces)g(coincide)g(with)f(the)g(Sob)s(olev)g
(spaces)h Fn(W)2926 3945 y Fk(1)p Fm(;q)3019 3982 y FA(\(\012\).)42
b(W)-8 b(e)28 b(de\014ne)120 4126 y Fn(H)209 4079 y Fm(s;q)201
4154 y(k)331 4126 y FA(as)33 b(the)g(closure)h(in)f Fn(H)1148
4090 y Fm(s;q)1270 4126 y FA(of)f(the)h(set)814 4263
y Fi(\010)872 4344 y Fn(u)p Fl(j)956 4359 y Fk(\012)1038
4344 y FA(:)28 b Fn(u)f Fl(2)h Fn(C)1347 4303 y Fh(1)1340
4368 y Fk(0)1421 4344 y FA(\()p Fj(R)1531 4303 y Fk(2)1571
4344 y FA(\))p Fn(;)33 b FA(supp)18 b Fn(u)j Fl(\\)2053
4263 y Fi(\000)p 2099 4264 71 4 v 81 x FA(\012)h Fl(n)g
FA(\(\012)h Fl([)f FA(\000)2543 4359 y Fm(k)2586 4344
y FA(\))2624 4263 y Fi(\001)2697 4344 y FA(=)28 b Fl(;)2851
4263 y Fi(\011)2925 4344 y Fn(:)120 4562 y FA(If)f Fn(s)h
Fl(2)g FA([)p Fl(\000)p FA(1)p Fn(;)17 b FA(0[,)29 b(then)f
Fn(H)1015 4514 y Fm(s;q)1007 4589 y(k)1132 4562 y FA(denotes)h(the)e
(dual)h(to)f Fn(H)2057 4514 y Fh(\000)p Fm(s;q)2199 4491
y Fg(0)2049 4589 y Fm(k)2224 4562 y FA(,)i(where)2567
4522 y Fk(1)p 2567 4539 36 4 v 2568 4596 a Fm(q)2623
4562 y FA(+)2732 4522 y Fk(1)p 2721 4539 57 4 v 2721
4596 a Fm(q)2755 4577 y Fg(0)2815 4562 y FA(=)e(1.)42
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4670 y Fm(s;q)483 4706 y FA(=)g Fn(H)690 4670 y Fm(s;q)807
4706 y Fl(\002)29 b Fn(:::)f Fl(\002)g Fn(H)1216 4670
y Fm(s;q)1347 4706 y FA(the)41 b Fn(l)i FA(times)f(direct)f(pro)s(duct)
g(of)g(the)g(spaces)h Fn(H)3214 4670 y Fm(s;q)3345 4706
y FA(and)f(b)m(y)120 4851 y Fr(H)208 4803 y Fm(s;q)208
4875 y Fk(0)326 4851 y FA(=)27 b Fn(H)518 4803 y Fm(s;q)510
4875 y Fk(1)630 4851 y Fl(\002)c Fn(:::)f Fl(\002)h Fn(H)1022
4803 y Fm(s;q)1014 4878 y(l)1144 4851 y FA(the)33 b(direct)g(pro)s
(duct)g(of)f(the)h(spaces)i Fn(H)2622 4803 y Fm(s;q)2614
4878 y(k)2711 4851 y FA(.)120 5042 y(Apart)30 b(of)f(the)i(real)f
(function)h(spaces)g(w)m(e)g(in)m(tro)s(duce)g(their)g(complex)g
(analoga:)42 b(If)30 b Fn(Z)36 b FA(is)31 b(a)f(real)120
5187 y(Banac)m(h)j(space,)h(w)m(e)g(denote)f(b)m(y)1367
5161 y Fi(e)1349 5187 y Fn(Z)40 b FA(its)33 b(complexi\014cation.)120
5378 y(F)-8 b(or)32 b(t)m(w)m(o)i(Banac)m(h)f(spaces)i
Fn(X)40 b FA(and)33 b Fn(Y)55 b FA(w)m(e)33 b(denote)h(the)f(space)h
(of)f(linear,)g(b)s(ounded)h(op)s(erators)120 5523 y(from)45
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Fn(X)57 b FA(=)49 b Fn(Y)21 b FA(,)49 b(then)c(w)m(e)i(abbreviate)f
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Fl(\032)50 b Fn(Y)p 120 5702 3526 4 v 290 5823 a Fx(Preprin)n(t)26
b(765,)h(W)-7 b(eierstra\031{Institut)26 b(f)1556 5827
y(\177)1554 5823 y(ur)i(Angew)n(andte)f(Analysis)g(und)h(Sto)r(c)n
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%%Page: 5 7
5 6 bop 120 144 a Fs(Classical)38 b(Solutions)g(of)g(Quasilinear)g(P)-9
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Fn(t)789 619 y Fk(1)829 604 y Fn(;)17 b(t)908 619 y Fk(2)947
604 y FA(];)g Fn(X)8 b FA(\))p Fn(;)114 b(C)1363 563
y Fm(\021)1405 604 y FA(\([)p Fn(t)1505 619 y Fk(1)1545
604 y Fn(;)17 b(t)1624 619 y Fk(2)1663 604 y FA(];)g
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y FA(\([)p Fn(t)2218 619 y Fk(1)2258 604 y Fn(;)17 b(t)2337
619 y Fk(2)2376 604 y FA(];)g Fn(X)8 b FA(\))p Fn(;)211
b(\021)32 b Fl(2)p FA(]0)p Fn(;)17 b FA(1[)120 825 y(denote)29
b(the)f(spaces)i(of)e(con)m(tin)m(uous,)j(H)1580 829
y(\177)1580 825 y(older)d(con)m(tin)m(uous,)j(and)d(once)h(con)m(tin)m
(uously)h(di\013eren-)120 969 y(tiable)c(functions,)j(resp)s(ectiv)m
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b([)p Fn(t)2351 984 y Fk(1)2391 969 y Fn(;)17 b(t)2470
984 y Fk(2)2509 969 y FA(])26 b(with)h(v)-5 b(alues)27
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FA(.)53 b(The)37 b(sym)m(b)s(ols)h Fl(h\001)o Fn(;)17
b Fl(\001)o(i)1309 1130 y Ff(R)1357 1111 y Fe(2)1432
1114 y FA(and)36 b Fl(h\001)o Fn(;)17 b Fl(\001)o(i)1801
1130 y Ff(C)1849 1111 y Fe(2)1924 1114 y FA(denote)36
b(the)h(canonic)f(bilinear)h(forms)f(on)g Fj(R)3607 1077
y Fk(2)120 1258 y FA(and)d Fj(C)382 1222 y Fk(2)421 1258
y FA(,)g(resp)s(ectiv)m(ely)-8 b(.)120 1466 y Fr(2.3)35
b(Assumption.)41 b Fn(\026)1012 1481 y Fm(k)1099 1466
y FA(:)j(\012)29 b Fl(\000)-17 b(!)28 b(B)s FA(\()p Fj(R)1635
1430 y Fk(2)1675 1466 y FA(\))p Fn(;)i(k)h Fl(2)d(f)p
FA(1)p Fn(;)17 b(:)g(:)g(:)e(;)i(l)r Fl(g)31 b FA(are)f(measurable)i
(mappings)g(in)m(to)120 1610 y(the)h(set)g(of)f(real,)h(symmetric)i(2)
22 b Fl(\002)g FA(2)33 b(matrices,)h(satisfying)f(the)g(relations)838
1815 y(max)773 1882 y Fm(k)r Fh(2f)p Fk(1)p Fm(;:::)o(;l)q
Fh(g)1101 1815 y FA(vraimax)1205 1877 y Fm(x)p Fh(2)p
Fk(\012)1475 1815 y Fl(k)p Fn(\026)1584 1830 y Fm(k)1627
1815 y FA(\()p Fn(x)p FA(\))p Fl(k)1808 1832 y Fh(B)r
Fk(\()p Ff(R)1931 1813 y Fe(2)1966 1832 y Fk(\))2025
1815 y Fl(\024)28 b Fn(\026)2189 1774 y Fh(\017)853 2043
y FA(min)778 2109 y Fm(k)r Fh(2f)p Fk(1)p Fm(;:::)o(;l)q
Fh(g)1106 2043 y FA(vraimin)1201 2105 y Fm(x)p Fh(2)p
Fk(\012)1462 2043 y Fl(h)p Fn(\026)1560 2058 y Fm(k)1602
2043 y FA(\()p Fn(x)p FA(\))p Fn(\030)5 b(;)17 b(\030)5
b Fl(i)1912 2059 y Ff(R)1960 2040 y Fe(2)2025 2043 y
Fl(\025)28 b Fn(\026)2189 2058 y Fh(\017)2228 2043 y
Fl(k)p Fn(\030)5 b Fl(k)2376 2002 y Fk(2)2376 2068 y
Ff(R)2424 2050 y Fe(2)2657 2043 y Fl(8)p Fn(\030)32 b
Fl(2)d Fj(R)2954 2002 y Fk(2)3445 1950 y FA(\(2.1\))120
2290 y(for)j(t)m(w)m(o)h(strictly)h(p)s(ositiv)m(e)g(constan)m(ts)g
Fn(\026)1639 2305 y Fh(\017)1711 2290 y FA(and)e Fn(\026)1959
2253 y Fh(\017)1998 2290 y FA(.)120 2497 y Fr(2.4)38
b(De\014nition.)k FA(F)-8 b(or)32 b(eac)m(h)h Fn(k)e
Fl(2)d(f)p FA(1)p Fn(;)17 b(:)g(:)g(:)e(;)i(l)r Fl(g)33
b FA(w)m(e)g(de\014ne)h(the)f(op)s(erator)1449 2718 y
Fn(a)1500 2733 y Fm(k)1598 2718 y FA(:)1703 2693 y Fi(e)1681
2718 y Fn(H)1770 2671 y Fk(1)p Fm(;)p Fk(2)1762 2746
y Fm(k)1891 2718 y Fl(\000)-16 b(!)2101 2693 y Fi(e)2079
2718 y Fn(H)2168 2671 y Fh(\000)p Fk(1)p Fm(;)p Fk(2)2160
2746 y Fm(k)3445 2718 y FA(\(2.2\))120 2939 y(b)m(y)1120
3102 y Fl(h)p Fn(a)1210 3117 y Fm(k)1252 3102 y Fn( )1315
3117 y Fk(1)1355 3102 y Fn(;)17 b( )1462 3117 y Fk(2)1502
3102 y Fl(i)44 b FA(=)1705 2966 y Fi(Z)1760 3192 y Fk(\012)1815
3102 y Fl(h)p Fn(\026)1913 3117 y Fm(k)1955 3102 y Fl(r)p
Fn( )2101 3117 y Fk(1)2141 3102 y Fn(;)17 b Fl(r)p Fn( )2331
3117 y Fk(2)2371 3102 y Fl(i)2410 3119 y Ff(C)2458 3100
y Fe(2)2513 3102 y Fn(dx;)799 b FA(\(2.3\))120 3341 y(where)34
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3316 y Fi(e)2975 3341 y Fn(H)3064 3294 y Fk(1)p Fm(;)p
Fk(2)3056 3369 y Fm(k)3191 3341 y FA(and)3403 3316 y
Fi(e)3381 3341 y Fn(H)3470 3294 y Fh(\000)p Fk(1)p Fm(;)p
Fk(2)3462 3369 y Fm(k)3619 3341 y FA(.)120 3486 y(F)-8
b(urther,)33 b(w)m(e)g(denote)h(b)m(y)f Fr(a)g FA(the)g(op)s(erator)876
3681 y Fi(e)860 3707 y Fr(H)948 3660 y Fk(1)p Fm(;)p
Fk(2)948 3731 y(0)1069 3707 y Fl(3)28 b FA(\()p Fn( )1264
3722 y Fk(1)1304 3707 y Fn(;)17 b(:)g(:)g(:)f(;)h( )1586
3722 y Fm(l)1612 3707 y FA(\))28 b Fl(7\000)-16 b(!)27
b FA(\()p Fn(a)1955 3722 y Fk(1)1995 3707 y Fn( )2058
3722 y Fk(1)2097 3707 y Fn(;)17 b(:)g(:)g(:)f(;)h(a)2367
3722 y Fm(l)2393 3707 y Fn( )2456 3722 y Fm(l)2483 3707
y FA(\))27 b Fl(2)2658 3681 y Fi(e)2642 3707 y Fr(H)2730
3660 y Fh(\000)p Fk(1)p Fm(;)p Fk(2)2730 3731 y(0)2879
3707 y Fn(:)539 b FA(\(2.4\))120 3928 y(The)35 b(restrictions)h(of)e
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y FA(,)g Fn(k)f Fl(2)d(f)p FA(1)p Fn(;)17 b(:)g(:)g(:)e(;)i(l)r
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4072 y FA(and)27 b Fr(H)392 4025 y Fk(1)p Fm(;)p Fk(2)392
4097 y(0)486 4072 y FA(,)g(resp)s(ectiv)m(ely)-8 b(,)31
b(map)c(in)m(to)g(the)g(\(real\))f(spaces)i Fn(H)2292
4025 y Fh(\000)p Fk(1)p Fm(;)p Fk(2)2284 4100 y Fm(k)2468
4072 y FA(and)e Fr(H)2739 4025 y Fh(\000)p Fk(1)p Fm(;)p
Fk(2)2739 4097 y(0)2888 4072 y FA(,)i(resp)s(ectiv)m(ely)-8
b(,)31 b(and)120 4217 y(will)i(b)s(e)g(denoted)h(b)m(y)f(the)g(same)g
(sym)m(b)s(ols.)120 4424 y Fr(2.5)46 b(De\014nition.)g
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(er)h(from)d(the)i(in)m(terv)-5 b(al)41 b(]1)p Fn(;)17
b Fl(1)p FA([.)65 b(Then)120 4569 y(for)37 b(eac)m(h)i
Fn(k)h Fl(2)d(f)p FA(1)p Fn(;)17 b(:)g(:)g(:)f(;)h(l)r
Fl(g)37 b FA(w)m(e)i(de\014ne)h(the)e(follo)m(wing)g(restriction)h(of)f
(the)g(op)s(erator)f Fn(a)3367 4584 y Fm(k)3448 4569
y FA(from)120 4713 y(De\014nition)c(2.4:)612 4934 y Fn(A)685
4949 y Fm(k)783 4934 y FA(:)55 b Fn( )32 b Fl(7!)27 b
Fn(a)1138 4949 y Fm(k)1181 4934 y Fn( )199 b( )32 b Fl(2)c
FA(dom)17 b Fn(A)1906 4949 y Fm(k)1976 4934 y FA(=)2080
4823 y Fi(n)2146 4934 y Fn( )32 b Fl(2)2357 4909 y Fi(e)2335
4934 y Fn(H)2424 4887 y Fk(1)p Fm(;)p Fk(2)2416 4962
y Fm(k)2573 4934 y FA(:)56 b Fn(a)2707 4949 y Fm(k)2749
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4893 y Fm(p)3044 4823 y Fi(o)3127 4934 y Fn(:)291 b FA(\(2.5\))120
5155 y(F)-8 b(urther,)33 b(w)m(e)g(de\014ne)603 5360
y Fr(A)55 b FA(:)g Fl(D)30 b FA(:=)e(dom)17 b Fr(A)27
b FA(=)h(dom)17 b Fn(A)1754 5375 y Fk(1)1815 5360 y Fl(\002)23
b Fn(:)17 b(:)g(:)22 b Fl(\002)g FA(dom)17 b Fn(A)2425
5375 y Fm(l)2479 5360 y Fl(\000)-16 b(!)2673 5334 y Fi(e)2667
5360 y Fr(L)2734 5319 y Fm(p)603 5529 y Fl(D)30 b(3)e
FA(\()p Fn( )905 5544 y Fk(1)945 5529 y Fn(;)17 b(:)g(:)g(:)f(;)h( )
1227 5544 y Fm(l)1253 5529 y FA(\))27 b Fl(7\000)-16
b(!)28 b Fr(A)p FA(\()p Fn( )1693 5544 y Fk(1)1732 5529
y Fn(;)17 b(:)g(:)g(:)f(;)h( )2014 5544 y Fm(l)2040 5529
y FA(\))28 b(:=)f(\()p Fn(A)2347 5544 y Fk(1)2387 5529
y Fn( )2450 5544 y Fk(1)2490 5529 y Fn(;)17 b(:)g(:)g(:)e(;)i(A)2781
5544 y Fm(l)2807 5529 y Fn( )2870 5544 y Fm(l)2897 5529
y FA(\))27 b Fl(2)3062 5504 y Fi(e)3056 5529 y Fr(L)3123
5488 y Fm(p)3445 5441 y FA(\(2.6\))p 120 5702 V 290 5823
a Fx(Preprin)n(t)f(765,)h(W)-7 b(eierstra\031{Institut)26
b(f)1556 5827 y(\177)1554 5823 y(ur)i(Angew)n(andte)f(Analysis)g(und)h
(Sto)r(c)n(hastik,)f(Berlin)g(2002)p eop
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6 7 bop 120 144 a Fr(6)174 b Fs(Hans-Christoph)37 b(Kaiser,)g(Ha)n(gen)
g(Neidhardt,)h(and)g(Jo)n(a)n(chim)h(Rehber)n(g)p 120
183 3526 4 v 120 383 a FA(The)46 b(domain)g(of)f(the)g(op)s(erator)g
Fn(A)1476 398 y Fm(k)1564 383 y FA(will)h(b)s(e)f(equipp)s(ed)i(with)f
(the)g(norm)f Fl(k)p FA(\()p Fn(A)3180 398 y Fm(k)3254
383 y FA(+)30 b(1\))17 b Fl(\001)g(k)3565 397 y Fd(e)3559
413 y Fm(L)3607 395 y Fc(p)120 527 y FA(whic)m(h)35 b(is)f(equiv)-5
b(alen)m(t)35 b(to)d(the)i(graph)f(norm)h(of)e Fn(A)1968
542 y Fm(k)2011 527 y FA(.)46 b(The)34 b(restrictions)h(of)d(the)i(op)s
(erators)f Fn(A)3576 542 y Fm(k)3619 527 y FA(,)120 672
y Fn(k)45 b Fl(2)c(f)p FA(1)p Fn(;)17 b(:)g(:)g(:)f(;)h(l)r
Fl(g)40 b FA(and)h Fr(A)f FA(to)g(the)i(real)e(domains)i(map)f(in)m(to)
f(the)i(\(real\))e(spaces)i Fn(L)3233 636 y Fm(p)3314
672 y FA(and)f Fr(L)3579 636 y Fm(p)3619 672 y FA(,)120
816 y(resp)s(ectiv)m(ely)-8 b(,)36 b(and)c(will)i(b)s(e)e(denoted)i(b)m
(y)f(the)g(same)h(sym)m(b)s(ols.)120 1033 y Fr(2.6)41
b(Remark.)j FA(De\014nition)36 b(2.4)f(incorp)s(orates)h(in)g(the)g
(usual)g(w)m(a)m(y)-8 b(,)38 b(cf.)52 b([5])36 b(or)f([2],)h(homoge-)
120 1177 y(neous)i(Neumann)g(b)s(oundary)g(conditions)g(on)f(\000)1958
1192 y Fm(k)2037 1177 y FA(and)g(homogeneous)i(Diric)m(hlet)e(b)s
(oundary)120 1322 y(conditions)d(on)e Fn(@)5 b FA(\012)24
b Fl(n)e FA(\000)1005 1337 y Fm(k)1080 1322 y FA(for)32
b(functions)h(from)g(dom)16 b Fn(A)2153 1337 y Fm(k)2196
1322 y FA(,)33 b Fn(k)e Fl(2)d(f)p FA(1)p Fn(;)17 b(:)g(:)g(:)e(;)i(l)r
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b(analytic)i(to)t(ols)120 2027 y FA(W)-8 b(e)24 b(outline)g(in)f(this)h
(section)h(the)f(functional)g(analytic)g(bac)m(kground)g(of)f(our)g(in)
m(v)m(estigation.)43 b(In)120 2171 y(particular,)33 b(w)m(e)h(sp)s
(ecify)g(the)g(adequate)g(Banac)m(h)f(spaces)i(for)d(the)h
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b(start)g(b)m(y)g(quoting)g(a)f(recen)m(tly)i(obtained)120
2460 y(in)m(terp)s(olation)f(result)h(for)e(spaces)i(represen)m(ting)h
(mixed)f(b)s(oundary)f(conditions)h(and)f(gather)120
2605 y(some)29 b(regularit)m(y)g(results)g(on)f(elliptic)h(and)f(parab)
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2749 y(w)m(e)34 b(supp)s(ose)g Fn(k)c Fl(2)e(f)p FA(1)p
Fn(;)17 b(:)g(:)g(:)f(;)h(l)r Fl(g)32 b FA(and)h(Assumption)h(2.1,)e
(and)h(Assumption)h(2.3)e(apply)-8 b(.)120 2966 y Fr(3.1)38
b(Prop)s(osition.)j Fs([6].)k Fo(If)695 3197 y Fn(\022)31
b Fl(2)p FA(]0)p Fn(;)17 b FA(1[)p Fn(;)215 b(q)32 b
Fl(2)p FA(]1)p Fn(;)17 b Fl(1)p FA([)p Fn(;)216 b(s)1952
3212 y Fk(0)1991 3197 y Fn(;)33 b(s)2097 3212 y Fk(1)2164
3197 y Fl(2)28 b FA([)p Fl(\000)p FA(1)p Fn(;)17 b FA(1])23
b Fl(n)2625 3087 y Fi(n)2692 3197 y Fl(\000)2790 3158
y Fk(1)p 2779 3174 57 4 v 2779 3232 a Fm(q)2813 3213
y Fg(0)2846 3197 y Fn(;)2916 3158 y Fk(1)p 2916 3174
36 4 v 2917 3232 a Fm(q)2961 3087 y Fi(o)3044 3197 y
Fn(;)120 3429 y Fo(then)35 b(ther)-5 b(e)35 b(is)f(the)h(fol)5
b(lowing)33 b(c)-5 b(omplex)34 b(interp)-5 b(olation)34
b(identity:)886 3549 y Fi(h)955 3635 y(e)933 3660 y Fn(H)1022
3613 y Fm(s)1055 3622 y Fe(0)1089 3613 y Fm(;q)1014 3688
y(k)1146 3660 y Fn(;)1212 3635 y Fi(e)1190 3660 y Fn(H)1279
3613 y Fm(s)1312 3622 y Fe(1)1346 3613 y Fm(;q)1271 3688
y(k)1403 3549 y Fi(i)1450 3729 y Fm(\022)1517 3660 y
FA(=)1643 3635 y Fi(e)1621 3660 y Fn(H)1710 3613 y Fm(s;q)1702
3688 y(k)1799 3660 y Fn(;)216 b(s)28 b FA(=)f(\(1)22
b Fl(\000)h Fn(\022)s FA(\))p Fn(s)2560 3675 y Fk(0)2622
3660 y FA(+)f Fn(\022)s(s)2814 3675 y Fk(1)2853 3660
y Fn(:)565 b FA(\(3.1\))120 3891 y Fr(3.2)38 b(Prop)s(osition.)j
Fs([11].)k Fo(F)-7 b(or)34 b(e)-5 b(ach)34 b Fn(k)d Fl(2)d(f)p
FA(1)p Fn(;)17 b(:)g(:)g(:)e(;)i(l)r Fl(g)35 b Fo(ther)-5
b(e)35 b(is)f(a)h(numb)-5 b(er)1422 4123 y Fn(q)1465
4138 y Fm(k)1536 4123 y FA(=)27 b Fn(q)1682 4138 y Fm(k)1725
4123 y FA(\(\012)p Fn(;)17 b FA(\000)1938 4138 y Fm(k)1981
4123 y Fn(;)g(\026)2084 4138 y Fm(k)2126 4123 y FA(\))28
b Fn(>)f FA(2)120 4354 y Fo(such)35 b(that)g(for)g(any)f
Fn(q)e Fl(2)c FA([2)p Fn(;)17 b(q)1215 4369 y Fm(k)1257
4354 y FA(])245 4618 y Fo(i\))49 b(the)i(maximal)f(r)-5
b(estriction)52 b(of)f(the)g(op)-5 b(er)g(ator)51 b Fn(a)2200
4633 y Fm(k)2295 4618 y Fo(fr)-5 b(om)50 b(De\014nition)h(2.4)g(which)f
(stil)5 b(l)364 4762 y(maps)48 b(into)869 4737 y Fi(e)847
4762 y Fn(H)936 4715 y Fh(\000)p Fk(1)p Fm(;q)928 4790
y(k)1132 4762 y Fo(pr)-5 b(ovides)47 b(a)i(top)-5 b(olo)g(gic)g(al)47
b(isomorphism|we)f(denote)i(it)h(also)f(by)364 4907 y
Fn(a)415 4922 y Fm(k)458 4907 y Fo(|b)-5 b(etwe)g(en)936
4882 y Fi(e)914 4907 y Fn(H)1003 4860 y Fk(1)p Fm(;q)995
4935 y(k)1130 4907 y Fo(and)1341 4882 y Fi(e)1319 4907
y Fn(H)1408 4860 y Fh(\000)p Fk(1)p Fm(;q)1400 4935 y(k)1555
4907 y Fo(;)35 b(and)215 5131 y(ii\))49 b(the)41 b(ne)-5
b(gative)41 b(of)g(this)g(isomorphism)f(gener)-5 b(ates)41
b(an)g(analytic)g(semigr)-5 b(oup)41 b(on)3402 5105 y
Fi(e)3380 5131 y Fn(H)3469 5083 y Fh(\000)p Fk(1)p Fm(;q)3461
5158 y(k)3616 5131 y Fo(,)364 5275 y(i.e.)1120 5420 y
FA(sup)1105 5502 y Fh(<)p Fm(z)s Fh(\025)p Fk(0)1282
5420 y FA(\(1)22 b(+)g Fl(j)p Fn(z)t Fl(j)p FA(\))1632
5335 y Fi(\015)1632 5395 y(\015)1687 5420 y FA(\()p Fn(a)1776
5435 y Fm(k)1841 5420 y FA(+)g(1)g(+)g Fn(z)t FA(\))2195
5378 y Fh(\000)p Fk(1)2290 5335 y Fi(\015)2290 5395 y(\015)2345
5459 y Fh(B)r Fk(\()2436 5442 y Fd(e)2420 5459 y Fm(H)2483
5426 y Fg(\000)p Fe(1)p Fc(;q)2478 5482 y(k)2615 5459
y Fk(\))2675 5420 y Fn(<)27 b Fl(1)p Fn(:)540 b FA(\(3.2\))p
120 5702 3526 4 v 290 5823 a Fx(Preprin)n(t)26 b(765,)h(W)-7
b(eierstra\031{Institut)26 b(f)1556 5827 y(\177)1554
5823 y(ur)i(Angew)n(andte)f(Analysis)g(und)h(Sto)r(c)n(hastik,)f
(Berlin)g(2002)p eop
%%Page: 7 9
7 8 bop 120 144 a Fs(Classical)38 b(Solutions)g(of)g(Quasilinear)g(P)-9
b(arabolic)38 b(Systems)674 b Fr(7)p 120 183 3526 4 v
120 383 a(3.3)46 b(Remark.)g FA(The)41 b(n)m(um)m(b)s(ers)h
Fn(q)1425 398 y Fm(k)1507 383 y FA(ma)m(y)f(b)s(e)f(arbitrarily)g
(close)h(to)f(2,)h(ev)m(en)h(in)e(the)h(case)f(of)120
527 y(pure,)33 b(homogeneous)h(Diric)m(hlet)f(b)s(oundary)g
(conditions,)h(cf.)44 b([13)o(,)33 b Fl(x)p FA(5].)120
717 y Fr(3.4)g(Prop)s(osition.)39 b Fs([7,)34 b Fl(x)p
Fs(5].)43 b Fo(L)-5 b(et)32 b Fn(U)38 b Fl(2)28 b Fn(L)1722
681 y Fh(1)1829 717 y Fo(b)-5 b(e)30 b(a)h(function)g(with)g(strictly)h
(p)-5 b(ositive)31 b(essential)120 862 y(upp)-5 b(er)28
b(and)f(lower)h(b)-5 b(ounds)27 b Fn(U)1207 826 y Fh(\017)1276
862 y Fo(and)g Fn(U)1524 877 y Fh(\017)1564 862 y Fo(,)i(r)-5
b(esp)g(e)g(ctively.)42 b(If)28 b Fn(p)f Fl(2)p FA(]1)p
Fn(;)17 b Fl(1)p FA([)p Fo(,)29 b(and)f Fn(A)2970 877
y Fm(k)3013 862 y Fo(,)h Fn(k)i Fl(2)d(f)p FA(1)p Fn(;)17
b(:)g(:)g(:)e(;)i(l)r Fl(g)120 1006 y Fo(is)29 b(one)g(of)g(the)g(op)-5
b(er)g(ators)29 b(fr)-5 b(om)29 b(De\014nition)f(2.5,)i(then)f(the)g
(op)-5 b(er)g(ator)29 b Fn(U)10 b(A)2844 1021 y Fm(k)2917
1006 y Fo(is)29 b(densely)g(de\014ne)-5 b(d)120 1151
y(and)34 b(satis\014es)g(the)h(fol)5 b(lowing)34 b(r)-5
b(esolvent)34 b(estimate)h(for)f Fn(z)f Fl(2)28 b Fj(C)35
b Fo(with)f Fl(<)p Fn(z)f Fl(\025)28 b FA(0)p Fo(:)813
1294 y Fi(\015)813 1354 y(\015)868 1379 y FA(\()p Fn(U)10
b(A)1055 1394 y Fm(k)1121 1379 y FA(+)22 b(1)g(+)g Fn(z)t
FA(\))1475 1338 y Fh(\000)p Fk(1)1570 1294 y Fi(\015)1570
1354 y(\015)1625 1418 y Fh(B)r Fk(\()1706 1401 y Fd(e)1700
1418 y Fm(L)1748 1399 y Fc(p)1785 1418 y Fk(\))1861 1379
y Fl(\024)1992 1311 y Fn(U)2068 1275 y Fh(\017)p 1992
1356 117 4 v 1997 1447 a Fn(U)2063 1462 y Fh(\017)2146
1379 y FA(\003)2231 1238 y Fi(\022)2314 1311 y Fn(\026)2373
1275 y Fh(\017)p 2314 1356 99 4 v 2314 1447 a Fn(\026)2373
1462 y Fh(\017)2422 1379 y Fn(;)17 b(p)2515 1238 y Fi(\023)2755
1311 y FA(1)p 2642 1356 275 4 v 2642 1447 a(1)22 b(+)g
Fl(j)p Fn(z)t Fl(j)2926 1379 y Fn(;)492 b FA(\(3.3\))120
1607 y Fo(with)35 b(some)f(explicitly)g(given)g(c)-5
b(ontinuous)35 b(function)1278 1807 y FA(\003)55 b(:)h([1)p
Fn(;)17 b Fl(1)p FA([)p Fl(\002)p FA(]1)p Fn(;)g Fl(1)p
FA([)p Fl(\000)-17 b(!)p FA(]0)p Fn(;)17 b Fl(1)p FA([)p
Fn(:)120 2008 y Fr(3.5)32 b(Prop)s(osition.)39 b Fo(L)-5
b(et)31 b Fn(X)39 b Fo(b)-5 b(e)30 b(a)h(Banach)e(sp)-5
b(ac)g(e)30 b(and)g(let)h Fn(B)36 b Fo(b)-5 b(e)31 b(a)f(densely)h
(de\014ne)-5 b(d)29 b(op)-5 b(er)g(ator)120 2152 y(on)34
b Fn(X)43 b Fo(satisfying)35 b(the)f(r)-5 b(esolvent)35
b(estimate)1189 2352 y FA(sup)1144 2438 y Fm(t)p Fh(2)p
Fk([0)p Fm(;)p Fh(1)p Fk([)1381 2352 y FA(\(1)22 b(+)g
Fn(t)p FA(\))1678 2268 y Fi(\015)1678 2328 y(\015)1733
2352 y FA(\()p Fn(B)28 b FA(+)22 b Fn(t)p FA(\))2044
2311 y Fh(\000)p Fk(1)2138 2268 y Fi(\015)2138 2328 y(\015)2194
2392 y Fh(B)r Fk(\()p Fm(X)5 b Fk(\))2391 2352 y Fn(<)28
b Fl(1)p Fn(:)120 2598 y Fo(If)34 b FA(0)28 b Fl(\024)g
Fn(\013)g(<)g(\014)33 b Fl(\024)28 b FA(1)p Fo(,)35 b(then)1368
2743 y FA([)p Fn(X)r(;)17 b FA(dom)g Fn(B)5 b FA(])1829
2758 y Fm(\014)1904 2743 y Fn(,)-17 b Fl(!)28 b FA(dom)16
b Fn(B)2321 2702 y Fm(\013)2371 2743 y Fn(;)1047 b FA(\(3.4\))120
2922 y Fo(and)1368 3067 y FA(dom)17 b Fn(B)1648 3026
y Fm(\014)1723 3067 y Fn(,)-17 b Fl(!)27 b FA([)p Fn(X)r(;)17
b FA(dom)g Fn(B)5 b FA(])2321 3082 y Fm(\013)2371 3067
y Fn(;)1047 b FA(\(3.5\))120 3247 y Fo(the)35 b(domains)f(of)h
Fn(B)5 b Fo(,)35 b Fn(B)1009 3210 y Fm(\013)1059 3247
y Fo(,)g(and)f Fn(B)1392 3210 y Fm(\014)1475 3247 y Fo(b)-5
b(eing)34 b(top)-5 b(olo)g(gize)g(d)34 b(by)h(a)g(norm)g(e)-5
b(quivalent)34 b(to)h(the)h(gr)-5 b(aph)120 3391 y(norm)34
b(of)h(the)g(c)-5 b(orr)g(esp)g(onding)33 b(op)-5 b(er)g(ator.)120
3645 y(Pr)g(o)g(of.)48 b FA(The)34 b(assertions)g(are)f(obtained)g
(from)f([17,)g(1.15.2,)g(1.10.3,)g(and)h(1.3.3].)p 3575
3645 4 66 v 3579 3582 59 4 v 3579 3645 V 3637 3645 4
66 v 120 3835 a Fr(3.6)i(Lemma.)42 b Fo(L)-5 b(et)33
b Fn(X)41 b Fo(and)32 b Fn(Y)54 b Fo(b)-5 b(e)33 b(Banach)e(sp)-5
b(ac)g(es,)32 b(let)h(us)g(assume)f(that)i Fn(Y)54 b
Fo(emb)-5 b(e)g(ds)32 b(densely)120 3979 y(and)k(c)-5
b(ontinuously)37 b(into)g(X,)g(and)f(let)h Fn(B)54 b
FA(:)48 b Fn(Y)k Fl(!)31 b Fn(X)45 b Fo(b)-5 b(e)37 b(a)f(line)-5
b(ar,)37 b(top)-5 b(olo)g(gic)g(al)36 b(isomorphism)120
4124 y(which)e(satis\014es)1189 4268 y FA(sup)1144 4354
y Fm(t)p Fh(2)p Fk([0)p Fm(;)p Fh(1)p Fk([)1381 4268
y FA(\(1)22 b(+)g Fn(t)p FA(\))1678 4184 y Fi(\015)1678
4243 y(\015)1733 4268 y FA(\()p Fn(B)28 b FA(+)22 b Fn(t)p
FA(\))2044 4227 y Fh(\000)p Fk(1)2138 4184 y Fi(\015)2138
4243 y(\015)2194 4307 y Fh(B)r Fk(\()p Fm(X)5 b Fk(\))2391
4268 y Fn(<)28 b Fl(1)p Fn(:)823 b FA(\(3.6\))120 4493
y Fo(F)-7 b(urthermor)i(e,)35 b(let)h Fn(X)933 4508 y
Fk(0)1002 4493 y Fl(\033)30 b Fn(Y)57 b Fo(b)-5 b(e)36
b(another)f(Banach)f(sp)-5 b(ac)g(e)35 b(which)g(emb)-5
b(e)g(ds)35 b(c)-5 b(ontinuously)36 b(into)120 4638 y(the)f(c)-5
b(omplex)35 b(interp)-5 b(olation)34 b(sp)-5 b(ac)g(e)35
b FA([)p Fn(X)r(;)17 b(Y)k FA(])1740 4653 y Fm(\022)1815
4638 y Fo(for)35 b(some)g Fn(\022)c Fl(2)p FA(]0)p Fn(;)17
b FA(1[)p Fo(.)46 b(We)36 b(denote)f(the)g(maximal)120
4782 y(r)-5 b(estriction)42 b(of)f Fn(B)47 b Fo(which)42
b(maps)f(into)g Fn(X)1672 4797 y Fk(0)1754 4782 y Fo(by)h
Fn(B)1962 4797 y Fk(0)2001 4782 y Fo(.)66 b(As)42 b Fn(Y)62
b Fl(\032)42 b Fn(X)2570 4797 y Fk(0)2609 4782 y Fo(,)i(the)e(domain)e
(of)i Fn(B)3403 4797 y Fk(0)3484 4782 y Fo(is)g(a)120
4927 y(subsp)-5 b(ac)g(e)34 b(of)h Fn(X)707 4942 y Fk(0)746
4927 y Fo(.)45 b(We)35 b(assume)f(that)h(this)g(subsp)-5
b(ac)g(e)34 b(is)h(dense)f(in)g Fn(X)2690 4942 y Fk(0)2764
4927 y Fo(and)h(we)f(supp)-5 b(ose)1158 5127 y FA(sup)1112
5213 y Fm(t)p Fh(2)p Fk([0)p Fm(;)p Fh(1)p Fk([)1350
5127 y FA(\(1)21 b(+)h Fn(t)p FA(\))1646 5042 y Fi(\015)1646
5102 y(\015)1702 5127 y FA(\()p Fn(B)1814 5142 y Fk(0)1875
5127 y FA(+)g Fn(t)p FA(\))2046 5086 y Fh(\000)p Fk(1)2141
5042 y Fi(\015)2141 5102 y(\015)2196 5166 y Fh(B)r Fk(\()p
Fm(X)2329 5175 y Fe(0)2364 5166 y Fk(\))2423 5127 y Fn(<)28
b Fl(1)p Fn(:)791 b FA(\(3.7\))120 5378 y Fo(Then)35
b(b)-5 b(oth,)37 b Fn(B)693 5342 y Fm(\013)778 5378 y
Fo(and)f Fn(B)1048 5342 y Fm(\013)1043 5403 y Fk(0)1134
5378 y Fo(ar)-5 b(e)36 b(wel)5 b(l)36 b(de\014ne)-5 b(d)35
b(for)h(any)g Fn(\013)31 b Fl(2)f FA([0)p Fn(;)17 b FA(1])p
Fo(.)48 b(Mor)-5 b(e)g(over,)37 b(if)f Fn(\013)30 b(>)g
FA(1)23 b Fl(\000)h Fn(\022)s Fo(,)120 5523 y(then)35
b(the)g(c)-5 b(omplex)33 b(interp)-5 b(olation)34 b(sp)-5
b(ac)g(e)34 b FA([)p Fn(X)1803 5538 y Fk(0)1843 5523
y Fn(;)17 b FA(dom)f Fn(B)2161 5538 y Fk(0)2201 5523
y FA(])2228 5538 y Fm(\013)2312 5523 y Fo(c)-5 b(ontinuously)35
b(emb)-5 b(e)g(ds)34 b(into)h Fn(Y)21 b Fo(.)p 120 5702
3526 4 v 290 5823 a Fx(Preprin)n(t)26 b(765,)h(W)-7 b
(eierstra\031{Institut)26 b(f)1556 5827 y(\177)1554 5823
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%%Page: 9 11
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V 3129 3381 a FA(2)3445 3312 y(\(4.1\))120 3563 y(suc)m(h)34
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3821 y Fl(\\)24 b(f)p Fn( )69 b FA(:)c Fn( )36 b(>)d
FA(0)p Fl(g)p Fn(:)i FA(F)-8 b(or)364 3965 y(an)m(y)33
b(b)s(ounded)g(set)h Fn(M)k Fl(\032)28 b Fr(H)1424 3929
y Fk(1)p Fm(;q)1549 3965 y FA(there)34 b(is)1019 4189
y(min)944 4256 y Fm(k)r Fh(2f)p Fk(1)p Fm(;:::)o(;l)q
Fh(g)1567 4189 y FA(inf)1328 4256 y Fm(t)20 b Fh(2)f
Fk([)p Fm(T)1500 4265 y Fe(0)1535 4256 y Fm(;)11 b(T)1607
4265 y Fe(1)1642 4256 y Fk(],)22 b Fb(w)f Fh(2)e Fm(M)1997
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4189 y Fn(E)2414 4204 y Fm(k)2473 4189 y FA(\()p Fn(t;)e
Fr(w)r FA(\))f(\()p Fn(x)p FA(\))28 b Fn(>)g FA(0)p Fn(;)379
b FA(\(4.2\))364 4440 y(and)33 b(a)f(constan)m(t)h Fl(E)1081
4455 y Fm(M)1192 4440 y FA(suc)m(h)h(that)560 4664 y
Fl(k)p Fn(E)682 4679 y Fm(k)741 4664 y FA(\()p Fn(t)814
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y Fn(;)g Fr(w)2388 4904 y Fk(2)2455 4889 y Fl(2)c Fn(M)10
b FA(.)223 5111 y(ii\))49 b Fn(F)427 5126 y Fm(k)470
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5111 y Fn(;)17 b(T)1654 5126 y Fk(1)1693 5111 y FA(])23
b Fl(\002)h Fr(H)1932 5075 y Fk(1)p Fm(;q)2058 5111 y
FA(in)m(to)35 b(the)f(set)h Fn(H)2670 5075 y Fk(1)p Fm(;q)2786
5111 y Fl(\\)23 b(f)p Fn( )65 b FA(:)60 b Fn( )35 b(>)30
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b(b)s(ounded)g(set)h Fn(M)k Fl(\032)28 b Fr(H)1424 5219
y Fk(1)p Fm(;q)1549 5255 y FA(there)34 b(is)1118 5480
y(min)1044 5546 y Fm(k)r Fh(2f)p Fk(1)p Fm(;:::)n(;l)q
Fh(g)1667 5480 y FA(inf)1427 5546 y Fm(t)20 b Fh(2)g
Fk([)p Fm(T)1600 5555 y Fe(0)1634 5546 y Fm(;)12 b(T)1707
5555 y Fe(1)1741 5546 y Fk(],)23 b Fb(w)d Fh(2)g Fm(M)2107
5480 y FA(inf)2097 5542 y Fm(x)p Fh(2)p Fk(\012)2251
5480 y Fn(F)2314 5495 y Fm(k)2374 5480 y FA(\()p Fn(t;)d
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b FA(\(4.4\))p 120 5702 3526 4 v 290 5823 a Fx(Preprin)n(t)26
b(765,)h(W)-7 b(eierstra\031{Institut)26 b(f)1556 5827
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%%Page: 10 12
10 11 bop 120 144 a Fr(10)118 b Fs(Hans-Christoph)37
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Fl(F)1100 398 y Fm(M)1211 383 y FA(suc)m(h)h(that)542
631 y Fl(k)p Fn(F)655 646 y Fm(k)715 631 y FA(\()p Fn(t)788
646 y Fk(1)827 631 y Fn(;)17 b Fr(w)952 646 y Fk(1)991
631 y FA(\))22 b Fl(\000)h Fn(F)1214 646 y Fm(k)1274
631 y FA(\()o Fn(t)1346 646 y Fk(2)1386 631 y Fn(;)17
b Fr(w)1511 646 y Fk(2)1550 631 y FA(\))p Fl(k)1638 660
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646 y Fk(1)2251 631 y Fl(\000)23 b Fn(t)2386 646 y Fk(2)2426
631 y Fl(j)2454 590 y Fm(\021)2517 631 y FA(+)f Fl(k)p
Fr(w)2746 646 y Fk(1)2808 631 y Fl(\000)g Fr(w)2988 646
y Fk(2)3028 631 y Fl(k)3078 648 y Fb(H)3141 629 y Fe(1)p
Fc(;q)3229 631 y FA(\))178 b(\(4.5\))364 880 y(for)32
b(all)g Fn(k)f Fl(2)d(f)p FA(1)p Fn(;)17 b(:)g(:)g(:)f(;)h(l)r
Fl(g)p FA(,)32 b Fn(t)1317 895 y Fk(1)1357 880 y Fn(;)h(t)1452
895 y Fk(2)1519 880 y Fl(2)28 b FA([)p Fn(T)1697 895
y Fk(0)1737 880 y Fn(;)17 b(T)1838 895 y Fk(1)1877 880
y FA(])33 b(and)g Fr(w)2208 895 y Fk(1)2247 880 y Fn(;)g
Fr(w)2388 895 y Fk(2)2455 880 y Fl(2)c Fn(M)10 b FA(.)196
1114 y(iii\))49 b Fn(G)441 1129 y Fm(k)483 1114 y FA(,)38
b Fn(k)e Fl(2)f(f)p FA(1)p Fn(;)17 b(:)g(:)g(:)e(;)i(l)r
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1114 y Fn(;)17 b(T)1682 1129 y Fk(1)1721 1114 y FA(])25
b Fl(\002)g Fr(H)1963 1078 y Fk(1)p Fm(;q)2091 1114 y
FA(in)m(to)37 b Fn(L)2359 1078 y Fm(p)2399 1114 y FA(.)54
b(Moreo)m(v)m(er,)39 b(for)c(an)m(y)i(b)s(ounded)364
1259 y(set)c Fn(M)39 b Fl(\032)28 b Fr(H)842 1222 y Fk(1)p
Fm(;q)967 1259 y FA(there)33 b(is)g(a)g(constan)m(t)g
Fl(G)1848 1274 y Fm(M)1960 1259 y FA(suc)m(h)h(that)566
1507 y Fl(k)p Fn(G)693 1522 y Fm(k)752 1507 y FA(\()p
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1522 y Fk(1)2228 1507 y Fl(\000)22 b Fn(t)2362 1522 y
Fk(2)2402 1507 y Fl(j)2430 1466 y Fm(\021)2494 1507 y
FA(+)g Fl(k)p Fr(w)2723 1522 y Fk(1)2784 1507 y Fl(\000)h
Fr(w)2965 1522 y Fk(2)3004 1507 y Fl(k)3054 1524 y Fb(H)3117
1505 y Fe(1)p Fc(;q)3205 1507 y FA(\))202 b(\(4.6\))364
1755 y(for)32 b(all)g Fn(k)f Fl(2)d(f)p FA(1)p Fn(;)17
b(:)g(:)g(:)f(;)h(l)r Fl(g)p FA(,)32 b Fn(t)1317 1770
y Fk(1)1357 1755 y FA(,)g Fn(t)1451 1770 y Fk(2)1519
1755 y Fl(2)c FA([)p Fn(T)1697 1770 y Fk(0)1736 1755
y Fn(;)17 b(T)1837 1770 y Fk(1)1877 1755 y FA(],)32 b(and)h
Fr(w)2234 1770 y Fk(1)2274 1755 y FA(,)f Fr(w)2414 1770
y Fk(2)2481 1755 y Fl(2)c Fn(M)10 b FA(.)199 1990 y(iv\))49
b(There)41 b(are)e(functions)i(\010)1320 2005 y Fm(k)1403
1990 y Fl(2)f Fn(C)1586 1954 y Fm(\021)1628 1990 y FA(\([)p
Fn(T)1750 2005 y Fk(0)1789 1990 y Fn(;)17 b(T)1890 2005
y Fk(1)1930 1990 y FA(];)g Fn(H)2090 1954 y Fk(1)p Fm(;q)2182
1990 y FA(\))p Fn(;)39 b(k)k Fl(2)d(f)p FA(1)p Fn(;)17
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2134 y(inhomogeneous)c(Diric)m(hlet)g(b)s(oundary)g(conditions)g(for)f
(the)h Fn(u)2745 2160 y Fm(k)2787 2134 y FA(.)54 b(F)-8
b(or)35 b(all)i Fn(t)d Fl(2)g FA([)p Fn(T)3439 2149 y
Fk(0)3479 2134 y Fn(;)17 b(T)3580 2149 y Fk(1)3619 2134
y FA(])364 2279 y(the)32 b(distributional)h(deriv)-5
b(ativ)m(es)35 b Fl(r)21 b(\001)g FA(\()p Fn(\026)1874
2294 y Fm(k)1916 2279 y Fl(r)p FA(\010)2069 2294 y Fm(k)2112
2279 y FA(\()p Fn(t)p FA(\)\))32 b(b)s(elong)g(to)g Fn(L)2789
2243 y Fm(p)2861 2279 y FA(and)h(there)f(is)h(in)f(the)364
2423 y(sense)i(of)e(traces,)i(cf.)43 b([16,)33 b(Ch.)g(1],)852
2672 y(\010)922 2687 y Fm(k)965 2672 y FA(\()p Fn(t)p
FA(\))p Fl(j)1104 2701 y Fm(@)t Fk(\012)p Fh(n)p Fk(\000)1275
2713 y Fc(k)1346 2672 y FA(=)27 b Fn(\036)1507 2687 y
Fm(k)1549 2672 y FA(\()p Fn(t)p FA(\))98 b(and)g Fn(\027)28
b Fl(\001)22 b FA(\()p Fn(\026)2236 2687 y Fm(k)2279
2672 y Fl(r)p FA(\010)2432 2687 y Fm(k)2475 2672 y FA(\()p
Fn(t)p FA(\)\))27 b(=)h(0)97 b(on)33 b(\000)3098 2687
y Fm(k)3140 2672 y FA(.)364 2920 y(Moreo)m(v)m(er,)h(the)f(mapping)885
3168 y([)p Fn(T)969 3183 y Fk(0)1009 3168 y Fn(;)17 b(T)1110
3183 y Fk(1)1149 3168 y FA(])28 b Fl(3)g Fn(t)g Fl(7!)f(r)22
b(\001)g FA(\()p Fn(\026)1740 3183 y Fm(k)1783 3168 y
Fl(r)p FA(\010)1936 3183 y Fm(k)1979 3168 y FA(\()p Fn(t)p
FA(\)\))27 b Fl(2)h Fn(L)2315 3127 y Fm(p)2551 3168 y
Fn(k)i Fl(2)e(f)p FA(1)p Fn(;)17 b(:)g(:)g(:)f(;)h(l)r
Fl(g)364 3416 y FA(is)33 b(from)f Fn(C)769 3380 y Fm(\021)811
3416 y FA(\([)p Fn(T)933 3431 y Fk(0)973 3416 y Fn(;)17
b(T)1074 3431 y Fk(1)1113 3416 y FA(];)g Fn(L)1250 3380
y Fm(p)1290 3416 y FA(\))p Fn(:)33 b FA(F)-8 b(urther,)558
3690 y(\010)628 3705 y Fm(k)699 3690 y Fl(2)28 b Fn(C)870
3649 y Fk(1)909 3690 y FA(\([)p Fn(T)1031 3705 y Fk(0)1071
3690 y Fn(;)17 b(T)1172 3705 y Fk(1)1211 3690 y FA(];)g
Fn(L)1348 3649 y Fm(p)1388 3690 y FA(\))p Fn(;)1675 3623
y(@)5 b FA(\010)1801 3638 y Fm(k)p 1675 3667 171 4 v
1714 3758 a Fn(@)g(t)1882 3690 y Fl(2)28 b Fn(C)2053
3649 y Fm(\021)2095 3690 y FA(\([)p Fn(T)2217 3705 y
Fk(0)2257 3690 y Fn(;)17 b(T)2358 3705 y Fk(1)2397 3690
y FA(];)g Fn(L)2534 3649 y Fm(p)2574 3690 y FA(\))p Fn(;)212
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Fl(g)p Fn(:)364 3955 y FA(In)33 b(the)g(sequel)h(w)m(e)g(will)f(denote)
g(b)m(y)h Fr(\010)p FA(\()p Fn(t)p FA(\))f(the)g(v)m(ector)2407
3875 y Fi(\000)2453 3955 y FA(\010)2523 3970 y Fk(1)2563
3955 y FA(\()p Fn(t)p FA(\))p Fn(;)17 b(:)g(:)g(:)f(;)h
FA(\010)2963 3970 y Fm(l)2989 3955 y FA(\()p Fn(t)p FA(\))3100
3875 y Fi(\001)3146 3955 y Fn(:)226 4190 y FA(v\))49
b(If)41 b Fr(u)532 4205 y Fk(0)613 4190 y FA(=)h(\()p
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4190 y FA(\),)43 b(then)e Fr(u)1578 4205 y Fk(0)1646
4190 y Fl(\000)28 b Fr(\010)p FA(\()p Fn(T)1927 4205
y Fk(0)1967 4190 y FA(\))41 b(b)s(elongs)g(to)g(the)g(complex)i(in)m
(terp)s(olation)364 4334 y(space)633 4254 y Fi(\002)680
4309 y(e)674 4334 y Fr(L)741 4298 y Fm(p)781 4334 y Fn(;)17
b Fl(D)905 4254 y Fi(\003)946 4373 y Fm(\015)1031 4334
y FA(for)41 b(some)h(n)m(um)m(b)s(er)g Fn(\015)5 b FA(,)43
b(cf.)68 b(\(4.1\).)g(N.B.)42 b Fl(D)h FA(is)f(the)f(domain)g(of)f(the)
364 4479 y(op)s(erator)32 b Fr(A)g FA(from)g(De\014nition)h(2.5.)120
4712 y Fr(4.2)41 b(Remark.)j FA(In)36 b(the)g(formal)f(equation)i
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b(of)e(the)i(solution)f(while)h(this)f(dep)s(endence)j(here)d(seems)i
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y(this)d(is)f(not)g(the)g(case)h(as)f(op)s(erators)g(suc)m(h)h(as)f
(e.g.)60 b Fn(G)2178 5016 y Fm(k)2237 5001 y FA(\()p
Fn(t;)17 b Fr(u)p FA(\))37 b(:=)g Fl(kr)p Fr(u)p Fl(k)2876
4965 y Fk(2)2876 5034 y Ff(R)2924 5015 y Fe(2)p Fc(l)3020
5001 y FA(are)h(co)m(v)m(ered)i(b)m(y)120 5145 y(Assumption)34
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b FA(:)c([)p Fn(T)1312 5393 y Fk(0)1352 5378 y Fn(;)17
b(T)1453 5393 y Fk(1)1492 5378 y FA(])33 b Fl(\002)g
Fj(R)53 b Fl(!)p FA(]0)p Fn(;)17 b Fl(1)p FA([)47 b(b)s(e)h(a)f
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%%Page: 11 13
11 12 bop 120 144 a Fs(Classical)38 b(Solutions)g(of)g(Quasilinear)g(P)
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4 v 250 383 a FA(i\))49 b(for)32 b(an)m(y)h Fn(R)c(>)e
FA(0)33 b(there)g(is)1710 605 y(inf)1436 672 y Fk(\()p
Fm(t;s)p Fk(\))p Fh(2)p Fk([)p Fm(T)1676 681 y Fe(0)1711
672 y Fm(;T)1772 681 y Fe(1)1806 672 y Fk(])p Fh(\002)p
Fk([)p Fh(\000)p Fm(R;R)p Fk(])2118 605 y Fn(\030)5 b
FA(\()p Fn(t;)17 b(s)p FA(\))27 b Fn(>)h FA(0;)223 898
y(ii\))49 b(for)32 b(an)m(y)h(\014xed)h Fn(t)28 b Fl(2)g
FA([)p Fn(T)1174 913 y Fk(0)1214 898 y Fn(;)17 b(T)1315
913 y Fk(1)1354 898 y FA(])33 b(the)g(function)g Fn(\030)5
b FA(\()p Fn(t;)17 b Fl(\001)p FA(\))31 b(is)i(t)m(wice)h(di\013eren)m
(tiable;)196 1119 y(iii\))49 b(there)31 b(is)f(a)g(n)m(um)m(b)s(er)h
Fn(\021)g Fl(2)p FA(]0)p Fn(;)17 b FA(1])30 b(and)g(for)g(an)m(y)g
Fn(R)f(>)f FA(0)h(there)i(is)g(a)e(constan)m(t)i Fn(c)3162
1134 y Fm(R)3250 1119 y FA(suc)m(h)g(that)801 1341 y
Fl(j)p Fn(\030)5 b FA(\()p Fn(t)950 1356 y Fk(1)989 1341
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Fl(j)22 b FA(+)g Fl(j)o Fn(@)1752 1356 y Fk(2)1792 1341
y Fn(\030)5 b FA(\()p Fn(t)1913 1356 y Fk(1)1952 1341
y Fn(;)17 b(s)p FA(\))22 b Fl(\000)h Fn(@)2253 1356 y
Fk(2)2293 1341 y Fn(\030)5 b FA(\()p Fn(t)2414 1356 y
Fk(2)2453 1341 y Fn(;)17 b(s)p FA(\))p Fl(j)26 b(\024)j
Fn(c)2783 1356 y Fm(R)2840 1341 y Fl(j)p Fn(t)2903 1356
y Fk(1)2965 1341 y Fl(\000)22 b Fn(t)3099 1356 y Fk(2)3139
1341 y Fl(j)3167 1300 y Fm(\021)364 1564 y FA(for)32
b(all)g Fn(s)c Fl(2)g FA([)p Fl(\000)p Fn(R)q(;)17 b(R)q
FA(])33 b(and)g(all)f Fn(t)1534 1579 y Fk(1)1574 1564
y FA(,)h Fn(t)1669 1579 y Fk(2)1736 1564 y Fl(2)28 b
FA([)p Fn(T)1914 1579 y Fk(0)1954 1564 y Fn(;)17 b(T)2055
1579 y Fk(1)2094 1564 y FA(];)199 1785 y(iv\))49 b(for)32
b(an)m(y)h Fn(R)c(>)e FA(0)33 b(there)g(is)1589 2008
y(sup)1329 2093 y Fk(\()p Fm(t;s)p Fk(\))p Fh(2)p Fk([)p
Fm(T)1569 2102 y Fe(0)1604 2093 y Fm(;T)1665 2102 y Fe(1)1700
2093 y Fk(])p Fh(\002)p Fk([)p Fh(\000)p Fm(R;R)p Fk(])2012
1923 y Fi(\014)2012 1983 y(\014)2045 2008 y Fn(@)2101
1966 y Fk(2)2096 2032 y(2)2141 2008 y Fn(\030)5 b FA(\()p
Fn(t;)17 b(s)p FA(\))2390 1923 y Fi(\014)2390 1983 y(\014)2450
2008 y Fn(<)28 b Fl(1)p Fn(:)120 2324 y FA(If)j Fn(w)f
Fl(2)e Fn(H)499 2287 y Fk(1)p Fm(;q)591 2324 y FA(,)j(2)d
Fn(<)f(q)32 b Fl(\024)c Fn(q)1052 2339 y Fk(1)1092 2324
y FA(,)j(and)g Fn(F)1401 2339 y Fk(1)1440 2324 y FA(\()p
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Fn(F)3134 2339 y Fk(1)3173 2324 y FA(\()p Fn(t;)17 b(w)s
FA(\)\()p Fn(x)p FA(\))11 b(:=)120 2468 y Fn(\030)168
2387 y Fi(\000)213 2468 y Fn(t;)17 b(w)s FA(\()p Fn(x)p
FA(\))496 2387 y Fi(\001)541 2468 y Fn(;)48 b FA(induced)i(b)m(y)f(the)
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FA(\),)50 b(then)f(the)f(mapping)h(\()p Fn(t;)17 b(w)s
FA(\))53 b Fl(7!)g Fn(E)3379 2483 y Fk(1)3419 2468 y
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Fn(:)28 b FA(The)120 3157 y(next)g(example)g(demonstrates)h(that)e
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Fn(E)3576 3172 y Fm(k)3619 3157 y FA(,)120 3302 y Fn(F)183
3317 y Fm(k)226 3302 y FA(,)k(and)h Fn(G)552 3317 y Fm(k)627
3302 y FA(to)f(Nem)m(ytzkii)j(op)s(erators.)120 3511
y Fr(4.4)k(Example.)44 b FA(Let)34 b(\000)1038 3526 y
Fh(\003)1111 3511 y FA(and)g Fn(\026)1361 3526 y Fh(\003)1434
3511 y FA(b)s(e)g(a)g(part)g(of)f Fn(@)5 b FA(\012)35
b(and)g(a)e(real)h(2)23 b Fl(\002)h FA(2)33 b(matrix)i(function)f(to)
120 3655 y(whic)m(h)41 b(apply)g(m)m(utatis)g(m)m(utandis)g(Assumption)
h(2.1)d(and)h(Assumption)h(2.3,)h(resp)s(ectiv)m(ely)-8
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3800 y FA(:)f Fn(H)741 3764 y Fk(1)p Fm(;)p Fk(2)733
3824 y Fh(\003)871 3800 y Fl(!)f Fn(H)1096 3764 y Fh(\000)p
Fk(1)p Fm(;)p Fk(2)1088 3824 y Fh(\003)1283 3800 y FA(b)s(e)i(the)g
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120 3944 y(let)k Fn(q)313 3959 y Fh(\003)394 3944 y FA(b)s(e)f(the)h
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Fa(F)3337 3959 y Fk(2)3418 3944 y FA(to)f(b)s(e)120 4089
y(mappings)c(from)f Fj(R)g FA(in)m(to)h(]0)p Fn(;)17
b Fl(1)p FA([)35 b(whic)m(h)j(are)e(either)h(m)m(ultiples)h(of)e(exp)s
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b(t)m(wice)f(con)m(tin)m(uously)h(di\013eren)m(tiable,)h(p)s
(olynomially)e(b)s(ounded)f(functions)h(\(e.g.)120 4378
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4615 y Fk(1)763 4600 y FA(,)g Fn(w)893 4615 y Fk(2)960
4600 y Fl(2)28 b Fn(H)1143 4559 y Fk(1)p Fm(;q)1235 4600
y FA(,)195 b Fn(d)28 b Fl(2)g Fn(H)1719 4559 y Fh(\000)p
Fk(1)p Fm(;q)1711 4625 y Fh(\003)1866 4600 y Fn(;)212
b FA(2)27 b Fn(<)h(q)j Fl(\024)e FA(min)17 b Fl(f)p Fn(q)2737
4615 y Fh(\003)2776 4600 y Fn(;)34 b(q)2880 4615 y Fk(1)2919
4600 y Fn(;)g(q)3023 4615 y Fk(2)3062 4600 y Fl(g)120
4822 y FA(b)s(e)c(giv)m(en,)i(and)e(let)g Fl(P)38 b FA(b)s(e)30
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Fn(w)2884 4837 y Fk(1)2924 4822 y Fn(;)17 b(w)3038 4837
y Fk(2)3076 4822 y FA(\))30 b(the)g(solution)120 4967
y Fn(')i FA(of)h(the)g(equation)1110 5111 y Fn(a)1161
5126 y Fh(\003)1201 5111 y Fn(')22 b FA(+)g Fa(F)1446
5126 y Fk(1)1485 5111 y FA(\()p Fn(w)1593 5126 y Fk(1)1654
5111 y FA(+)g Fn(')p FA(\))g Fl(\000)h Fa(F)2037 5126
y Fk(2)2076 5111 y FA(\()p Fn(w)2184 5126 y Fk(2)2245
5111 y Fl(\000)g Fn(')p FA(\))28 b(=)f Fn(d:)120 5300
y FA(This)34 b(solution)f(exists)h(and)f(is)g(unique)h(b)s(ecause)g
(the)f(op)s(erator)773 5523 y Fn(H)862 5482 y Fk(1)p
Fm(;)p Fk(2)854 5547 y Fh(\003)984 5523 y Fl(3)28 b Fn(')f
Fl(7!)h Fn(a)1348 5538 y Fh(\003)1387 5523 y Fn(')22
b FA(+)g Fa(F)1632 5538 y Fk(1)1672 5523 y FA(\()p Fn(w)1780
5538 y Fk(1)1841 5523 y FA(+)g Fn(')p FA(\))g Fl(\000)g
Fa(F)2223 5538 y Fk(2)2263 5523 y FA(\()p Fn(w)2371 5538
y Fk(2)2432 5523 y Fl(\000)h Fn(')p FA(\))k Fl(2)h Fn(H)2844
5482 y Fh(\000)p Fk(1)p Fm(;)p Fk(2)2836 5547 y Fh(\003)p
120 5702 V 290 5823 a Fx(Preprin)n(t)e(765,)h(W)-7 b
(eierstra\031{Institut)26 b(f)1556 5827 y(\177)1554 5823
y(ur)i(Angew)n(andte)f(Analysis)g(und)h(Sto)r(c)n(hastik,)f(Berlin)g
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12 13 bop 120 144 a Fr(12)118 b Fs(Hans-Christoph)37
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120 183 3526 4 v 120 383 a FA(is)g(w)m(ell)h(de\014ned)h(and)e
(strongly)g(monotone.)63 b(Moreo)m(v)m(er,)42 b(as)d
Fn(a)2497 398 y Fh(\003)2575 383 y FA(pro)m(vides)i(an)d(isomorphism)
120 527 y(b)s(et)m(w)m(een)d Fn(H)586 491 y Fk(1)p Fm(;q)578
552 y Fh(\003)710 527 y FA(and)e Fn(H)989 491 y Fh(\000)p
Fk(1)p Fm(;q)981 552 y Fh(\003)1136 527 y FA(,)g(cf.)43
b(Prop)s(osition)33 b(3.2,)f Fn(')h FA(ev)m(en)h(b)s(elongs)f(to)f
Fn(H)2925 491 y Fk(1)p Fm(;q)2917 552 y Fh(\003)3045
527 y Fl(\032)c Fn(H)3239 491 y Fk(1)p Fm(;q)3332 527
y FA(.)43 b(If)33 b(one)120 672 y(de\014nes)193 868 y
Fn(F)256 883 y Fk(1)295 787 y Fi(\000)341 868 y Fn(t;)17
b FA(\()p Fn(w)528 883 y Fk(1)567 868 y Fn(;)g(w)681
883 y Fk(2)720 868 y FA(\))758 787 y Fi(\001)831 868
y FA(:=)28 b Fa(F)1023 883 y Fk(1)1062 787 y Fi(\000)1108
868 y Fn(w)1178 883 y Fk(1)1239 868 y FA(+)22 b Fl(P)8
b FA(\()p Fn(w)1522 883 y Fk(1)1562 868 y Fn(;)17 b(w)1676
883 y Fk(2)1714 868 y FA(\))1752 787 y Fi(\001)1798 868
y Fn(;)114 b(F)2002 883 y Fk(2)2042 787 y Fi(\000)2087
868 y Fn(t;)17 b FA(\()p Fn(w)2274 883 y Fk(1)2314 868
y Fn(;)g(w)2428 883 y Fk(2)2466 868 y FA(\))2504 787
y Fi(\001)2578 868 y FA(:=)27 b Fa(F)2769 883 y Fk(2)2809
787 y Fi(\000)2854 868 y Fn(w)2924 883 y Fk(2)2986 868
y Fl(\000)22 b(P)8 b FA(\()p Fn(w)3270 883 y Fk(1)3310
868 y Fn(;)17 b(w)3424 883 y Fk(2)3463 868 y FA(\))3501
787 y Fi(\001)3546 868 y Fn(;)120 1064 y FA(then)33 b
Fn(F)405 1079 y Fk(1)445 1064 y FA(,)f Fn(F)567 1079
y Fk(2)639 1064 y FA(satisfy)i(Assumption)g(4.1.ii.)120
1250 y Fr(4.5)g(Remark.)40 b FA(The)31 b(imp)s(ortance)f(of)f(the)i
(\014rst)f(example)h(is)f(eviden)m(t.)45 b(The)30 b(second)h(example)
120 1394 y(pla)m(ys)39 b(a)e(role)h(in)f(the)h(theory)g(of)f(v)-5
b(an)38 b(Ro)s(osbro)s(ec)m(k's)g(system)i(whic)m(h)f(describ)s(es)g
(the)f(\015o)m(w)g(of)120 1539 y(electrons)45 b(and)e(holes)h(in)g
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b(Based)44 b(up)s(on)g(Theo-)120 1683 y(rem)29 b(5.10)g(w)m(e)h(shall)f
(deriv)m(e)i(a)e(lo)s(cal,)g(unique)i(solution)e(of)f(v)-5
b(an)29 b(Ro)s(osbro)s(ec)m(k's)h(system)h(on)e(t)m(w)m(o)120
1828 y(dimensional)34 b(domains)f(in)g(a)f(forthcoming)h(pap)s(er)g
([12)o(].)120 2014 y Fr(4.6)46 b(De\014nition.)g FA(W)-8
b(e)40 b(\014x)g(from)f(no)m(w)i(on)e(the)h(n)m(um)m(b)s(ers)i
Fn(q)t FA(,)f Fn(\021)t FA(,)g Fn(\015)5 b FA(,)42 b(and)d
Fn(p)h FA(:=)3155 1970 y Fm(q)p 3155 1991 36 4 v 3155
2048 a Fk(2)3239 2014 y FA(according)120 2158 y(to)d(Assumption)j(4.1)d
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2158 y FA(:)53 b(dom)17 b Fn(A)2280 2173 y Fm(k)2359
2158 y Fl(!)2503 2133 y Fi(e)2495 2158 y Fn(L)2561 2122
y Fm(p)2639 2158 y FA(and)37 b Fr(A)53 b FA(:)g Fl(D)39
b(!)3309 2133 y Fi(e)3303 2158 y Fr(L)3370 2122 y Fm(p)3448
2158 y FA(from)120 2303 y(De\014nition)30 b(2.5)f(alw)m(a)m(ys)i(will)f
(refer)g(to)f(this)h(n)m(um)m(b)s(er)h Fn(p)p FA(.)42
b(F)-8 b(urthermore,)31 b(let)f Fr(P)43 b FA(:)3146 2277
y Fi(e)3130 2303 y Fr(H)3218 2266 y Fk(1)p Fm(;q)3338
2303 y Fl(!)27 b Fr(H)3553 2266 y Fk(1)p Fm(;q)120 2447
y FA(b)s(e)k(the)g(mapping)g(on)m(to)f(the)h(real)f(part)h(of)1721
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2447 y FA(whic)m(h)h(tak)m(es)f(comp)s(onen)m(t)m(wise)j(the)d(real)f
(part)120 2592 y(of)36 b(the)g(function,)i(and)e(let)h
Fn(Q)50 b FA(:)h Fn(L)1429 2555 y Fm(p)1502 2592 y Fl(!)1644
2566 y Fi(e)1636 2592 y Fn(L)1702 2555 y Fm(p)1778 2592
y FA(b)s(e)36 b(the)h(canonic)g(em)m(b)s(edding)g(of)f(the)h(real)f
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2969 y(No)m(w)f(w)m(e)h(presen)m(t)g(a)e(precise)j(form)m(ulation)d(of)
g(the)h(formal)g(equations)g(\(1.1\).)120 3155 y Fr(4.7)44
b(De\014nition.)h FA(W)-8 b(e)39 b(sa)m(y)g(that)f Fr(u)f
FA(=)g Fr(v)28 b FA(+)d Fr(\010)38 b FA(is)h(a)f(lo)s(cal)g(solution)g
(of)45 b(\(1.1\))o(,)40 b(if)e(there)h(is)f(a)120 3300
y(solution)33 b Fr(v)h FA(to)f(the)g(follo)m(wing)120
3486 y Fr(4.8)38 b(Problem.)k FA(Determine)33 b(a)f(n)m(um)m(b)s(er)i
Fn(T)42 b Fl(2)p FA(])p Fn(T)1950 3501 y Fk(0)1990 3486
y Fn(;)17 b(T)2091 3501 y Fk(1)2130 3486 y FA(])33 b(and)f(a)h
(function)784 3682 y Fr(v)c Fl(2)f Fn(C)7 b FA(\([)p
Fn(T)1165 3697 y Fk(0)1205 3682 y Fn(;)17 b(T)d FA(])p
Fn(;)j Fr(L)1458 3641 y Fm(p)1497 3682 y FA(\))22 b Fl(\\)h
Fn(C)7 b FA(\(])p Fn(T)1845 3697 y Fk(0)1884 3682 y Fn(;)17
b(T)d FA(])p Fn(;)j Fr(P)p Fl(D)s FA(\))k Fl(\\)h Fn(C)2451
3641 y Fk(1)2491 3682 y FA(\(])p Fn(T)2613 3697 y Fk(0)2652
3682 y Fn(;)17 b(T)d FA(])p Fn(;)j Fr(L)2905 3641 y Fm(p)2944
3682 y FA(\))463 b(\(4.7\))120 3878 y(suc)m(h)34 b(that)1449
4022 y Fr(v)r FA(\()p Fn(T)1605 4037 y Fk(0)1644 4022
y FA(\))28 b(=)f Fr(u)1875 4037 y Fk(0)1937 4022 y Fl(\000)c
Fr(\010)p FA(\()p Fn(T)2213 4037 y Fk(0)2252 4022 y FA(\))p
Fn(;)1128 b FA(\(4.8\))120 4200 y(and)570 4329 y Fn(@)5
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4396 y FA(\()p Fn(t)p FA(\))22 b(+)g(\()p Fn(E)1068 4411
y Fm(k)1128 4396 y FA(\()o Fn(t;)17 b Fr(v)r FA(\()p
Fn(t)p FA(\))22 b(+)g Fr(\010)p FA(\()p Fn(t)p FA(\)\))17
b Fn(F)1846 4411 y Fm(k)1905 4396 y FA(\()p Fn(t;)g Fr(v)r
FA(\()p Fn(t)p FA(\))22 b(+)g Fr(\010)p FA(\()p Fn(t)p
FA(\)\))17 b Fn(A)2634 4411 y Fm(k)2699 4396 y FA(+)22
b(1\))16 b Fn(v)2947 4411 y Fm(k)2990 4396 y FA(\()p
Fn(t)p FA(\))866 4634 y(=)27 b Fn(v)1016 4649 y Fm(k)1059
4634 y FA(\()p Fn(t)p FA(\))22 b Fl(\000)1302 4567 y
Fn(@)5 b FA(\010)1428 4582 y Fm(k)p 1302 4611 171 4 v
1341 4703 a Fn(@)g(t)1482 4634 y FA(\()p Fn(t)p FA(\))860
4837 y(+)22 b Fn(E)1030 4852 y Fm(k)1090 4837 y FA(\()p
Fn(t;)17 b Fr(v)r FA(\()p Fn(t)p FA(\))k(+)h Fr(\010)p
FA(\()p Fn(t)p FA(\)\))17 b Fl(hr)p Fn(F)1930 4852 y
Fm(k)1989 4837 y FA(\()p Fn(t;)g Fr(v)r FA(\()p Fn(t)p
FA(\))22 b(+)g Fr(\010)p FA(\()p Fn(t)p FA(\)\))p Fn(;)17
b(\026)2731 4852 y Fm(k)2773 4837 y Fl(r)p Fn(v)2903
4852 y Fm(k)2946 4837 y FA(\()p Fn(t)p FA(\))p Fl(i)3096
4866 y Ff(R)3144 4847 y Fe(2)860 5006 y FA(+)22 b Fn(G)1035
5021 y Fm(k)1094 5006 y FA(\()p Fn(t;)17 b Fr(v)r FA(\()p
Fn(t)p FA(\))22 b(+)g Fr(\010)p FA(\()p Fn(t)p FA(\)\))860
5176 y Fl(\000)h Fn(E)1032 5191 y Fm(k)1091 5176 y FA(\()p
Fn(t;)17 b Fr(v)r FA(\()p Fn(t)p FA(\))22 b(+)g Fr(\010)p
FA(\()p Fn(t)p FA(\)\))17 b Fn(F)1810 5191 y Fm(k)1869
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b(+)g Fr(\010)p FA(\()p Fn(t)p FA(\)\))16 b Fl(r)23 b(\001)e
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y(+)h Fn(E)1030 5360 y Fm(k)1090 5345 y FA(\()p Fn(t;)17
b Fr(v)r FA(\()p Fn(t)p FA(\))k(+)h Fr(\010)p FA(\()p
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13 14 bop 120 144 a Fs(Classical)38 b(Solutions)g(of)g(Quasilinear)g(P)
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671 y Fm(k)1912 656 y FA(\))1182 826 y(=)28 b Fn(E)1358
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FA(\()p Fn(t;)h Fr(v)23 b FA(+)f Fr(\010)p FA(\))17 b
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b FA(+)e Fr(\010)p FA(\))p Fn(;)17 b(\026)3179 1010 y
Fm(k)3221 995 y Fl(r)p Fn(v)3351 1010 y Fm(k)3394 995
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Fn(A)2782 1258 y Fm(k)2825 1243 y FA(,)h(cf.)66 b(De\014nition)40
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2309 y Fi(e)2046 2334 y Fr(H)2134 2298 y Fk(1)p Fm(;q)2259
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2583 y FA(\()p Fn(t;)17 b Fr(Pw)q FA(\))g Fn(;)2523 2557
y Fi(e)2504 2583 y Fn(G)2581 2598 y Fm(k)2641 2583 y
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3064 y Fo(,)g(and)e FA(\010)2902 3079 y Fm(k)2945 3064
y Fo(,)i Fn(k)g Fl(2)d(f)p FA(1)p Fn(;)17 b(:)g(:)g(:)e(;)i(l)r
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y Fo(,)1655 3183 y Fi(e)1636 3208 y Fn(F)1699 3223 y
Fm(k)1742 3208 y Fo(,)1822 3183 y Fi(e)1803 3208 y Fn(G)1880
3223 y Fm(k)1923 3208 y Fo(,)i(and)e Fn(Q)p FA(\010)2317
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y Fm(k)3114 3633 y FA(and)g(the)g(v)m(ec-)120 3778 y(tor)281
3697 y Fi(\000)326 3778 y Fn(Q)p FA(\010)473 3793 y Fk(1)513
3778 y Fn(;)17 b(:)g(:)g(:)f(;)h(Q)p FA(\010)879 3793
y Fm(l)906 3697 y Fi(\001)987 3778 y FA(again)36 b(b)m(y)h(\010)1460
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3922 y(Assumption)e(4.1)e(w)m(e)i(implicitly)g(also)f(refer)g(to)f
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y Fr(L)1482 4362 y Fm(p)1522 4403 y FA(\))22 b Fl(\\)g
Fn(C)7 b FA(\(])p Fn(T)1869 4418 y Fk(0)1909 4403 y Fn(;)17
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4362 y Fk(1)2439 4403 y FA(\(])p Fn(T)2561 4418 y Fk(0)2600
4403 y Fn(;)17 b(T)d FA(])p Fn(;)2792 4378 y Fi(e)2786
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5224 y Fm(k)p 213 5254 147 4 v 240 5345 a Fn(@)g(t)370
5277 y FA(\()p Fn(t)p FA(\))22 b(+)601 5166 y Fi(\020)680
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b Fn(A)2298 5292 y Fm(k)2363 5277 y FA(+)22 b(1)2510
5166 y Fi(\021)2586 5277 y Fn(v)2633 5292 y Fm(k)2676
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Fm(k)3009 5277 y FA(\()p Fn(t;)17 b Fr(v)r FA(\()p Fn(t)p
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14 15 bop 120 144 a Fr(14)118 b Fs(Hans-Christoph)37
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885 y Fi(D)1449 996 y Fl(r)1551 970 y Fi(e)1532 996 y
Fn(F)1595 1011 y Fm(k)1654 996 y FA(\()p Fn(t;)17 b Fr(v)24
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996 y FA(\()p Fn(t)p FA(\))2634 885 y Fi(E)2695 1065
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b(3.7)f(applies)i(with)f Fn(X)45 b FA(:=)2708 2217 y
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2810 y Fn(;)17 b(T)1822 2825 y Fk(1)1862 2810 y FA(])22
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y Fk(1)p Fm(;q)2219 2810 y Fl(\000)-16 b(!)27 b(B)s FA(\()p
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y Fm(p)2744 2810 y FA(\))p Fn(;)718 3028 y Fl(D)k(3)d
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1342 3043 y Fm(l)1368 3028 y FA(\))28 b Fl(7\000)-16
b(!)27 b FA(\()p Fa(A)1731 3043 y Fk(1)1771 3028 y FA(\()p
Fn(t;)17 b Fr(w)r FA(\))p Fn( )2072 3043 y Fk(1)2111
3028 y Fn(;)g(:)g(:)g(:)f(;)h Fa(A)2401 3043 y Fm(l)2427
3028 y FA(\()p Fn(t;)g Fr(w)r FA(\))p Fn( )2728 3043
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y FA(where)373 3433 y Fa(A)444 3448 y Fm(k)487 3433 y
FA(\()p Fn(t;)17 b Fr(w)r FA(\))27 b(:=)h(1)21 b(+)1071
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y FA(\()p Fn(t;)c Fr(w)23 b FA(+)f Fr(\010)p FA(\()p
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3448 y Fm(k)1871 3433 y FA(\()p Fn(t;)17 b Fr(w)24 b
FA(+)e Fr(\010)p FA(\()p Fn(t)p FA(\)\))17 b Fn(A)2511
3448 y Fm(k)2553 3433 y Fn(;)212 b(k)31 b Fl(2)d(f)p
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y Fi(e)1157 4304 y Fn(E)1229 4319 y Fm(k)1289 4304 y
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4319 y Fk(0)1880 4304 y Fn(;)g Fr(u)1986 4319 y Fk(0)2025
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5161 y(tiv)m(e)h(essen)m(tial)h(lo)m(w)m(er)f(and)f(upp)s(er)h(b)s
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15 16 bop 120 144 a Fs(Classical)38 b(Solutions)g(of)g(Quasilinear)g(P)
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Fl(\001)17 b(k)1453 1144 y Fd(e)1447 1160 y Fm(L)1495
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1105 y(\015)1942 1049 y(\000)1988 1130 y FA(1)22 b(+)g
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Fl(\001)2423 1045 y Fi(\015)2423 1105 y(\015)2485 1152
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1389 y Fk(0)2014 1374 y Fn(:)120 1649 y FA(Ha)m(ving)45
b(an)g(application)g(of)g(Prop)s(osition)g(3.7)f(in)h(mind,)k(our)44
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Fl(A)1736 1808 y Fk(0)1814 1793 y FA(from)g(De\014nition)h(5.1.)61
b(Th)m(us,)41 b(w)m(e)f(also)e(will)i(b)s(e)120 1938
y(able)33 b(to)f(mak)m(e)i(use)f(of)g(Prop)s(osition)f(3.5)h(for)f(the)
h(op)s(erator)e Fn(B)i FA(:=)28 b Fl(A)2689 1953 y Fk(0)2728
1938 y FA(.)120 2165 y Fr(5.3)42 b(Theorem.)i Fo(The)38
b(domain)f Fl(D)j Fo(of)e(the)h(op)-5 b(er)g(ator)37
b Fl(A)2239 2180 y Fk(0)2317 2165 y Fo(fr)-5 b(om)37
b(De\014nition)g(5.1)h(is)g(dense)f(in)126 2284 y Fi(e)120
2310 y Fr(L)187 2273 y Fm(p)227 2310 y Fo(.)42 b(With)28
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2721 y FA(comp)s(onen)m(t)h(of)e(the)h(op)s(erator)f
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FA(:=)120 2865 y Fn(U)186 2880 y Fm(k)262 2865 y FA(=)390
2840 y Fi(e)371 2865 y Fn(E)443 2880 y Fm(k)502 2865
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2880 y Fk(0)782 2865 y FA(\))856 2840 y Fi(e)837 2865
y Fn(F)900 2880 y Fm(k)959 2865 y FA(\()p Fn(T)1054 2880
y Fk(0)1094 2865 y Fn(;)g Fr(u)1200 2880 y Fk(0)1239
2865 y FA(\).)53 b(According)36 b(to)g(Assumption)h(4.1.i)f(and)g
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3025 y Fm(k)796 3010 y FA(has)g(strictly)g(p)s(ositiv)m(e)h(essen)m
(tial)g(lo)m(w)m(er)g(and)e(upp)s(er)h(b)s(ounds;)i(N.B.)3349
2984 y Fi(e)3327 3010 y Fn(H)3416 2973 y Fk(1)p Fm(;q)3536
3010 y Fn(,)-17 b Fl(!)128 3129 y Fi(e)120 3154 y Fn(L)186
3118 y Fh(1)261 3154 y Fn(:)42 b FA(By)h(Prop)s(osition)f(3.4)g(no)m(w)
g(follo)m(ws)h(that)f Fn(U)2023 3169 y Fm(k)2066 3154
y Fn(A)2139 3169 y Fm(k)2223 3154 y FA(is)h(densely)h(de\014ned)f(and)g
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89 b(Hence,)53 b Fl(A)1683 3314 y Fk(0)1770 3299 y FA(is)48
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3443 y(estimate)34 b(\(3.9\))o(.)p 3575 3443 4 66 v 3579
3380 59 4 v 3579 3443 V 3637 3443 4 66 v 120 3671 a Fr(5.4)40
b(Theorem.)k Fo(F)-7 b(or)36 b(every)h Fn(\013)32 b Fl(2)p
FA(])1456 3631 y Fk(1)p 1456 3648 36 4 v 1456 3705 a(2)1526
3671 y FA(+)1635 3631 y Fk(1)p 1635 3648 V 1636 3705
a Fm(q)1680 3671 y Fn(;)17 b FA(1[)37 b Fo(the)g(sp)-5
b(ac)g(e)36 b FA(dom)17 b Fl(A)2538 3634 y Fm(\013)2538
3695 y Fk(0)2587 3671 y Fo(,)37 b(e)-5 b(quipp)g(e)g(d)37
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3854 y Fb(L)459 3835 y Fc(p)534 3824 y Fo(c)-5 b(ontinuously)34
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y Fr(H)1715 3776 y Fk(1)p Fm(;q)1715 3848 y Fk(0)1807
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4334 y(dom)17 b(\(1)22 b(+)g Fn(U)1332 4349 y Fm(k)1375
4334 y Fn(A)1448 4349 y Fm(k)1490 4334 y FA(\))1528 4286
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4334 y Fn(H)1832 4287 y Fk(1)p Fm(;q)1824 4362 y(k)2022
4334 y FA(for)32 b(all)h Fn(k)e Fl(2)d(f)p FA(1)p Fn(;)17
b(:)g(:)g(:)e(;)i(l)r Fl(g)p FA(.)537 b(\(5.4\))120 4579
y(Lemma)33 b(3.6)f(applies)i(to)e(this)i(situation)f(with)764
4823 y Fn(Y)49 b FA(:=)1023 4798 y Fi(e)1001 4823 y Fn(H)1090
4775 y Fk(1)p Fm(;q)1082 4850 y(k)1182 4823 y Fn(;)115
b(X)35 b FA(:=)1593 4798 y Fi(e)1571 4823 y Fn(H)1660
4775 y Fh(\000)p Fk(1)p Fm(;q)1652 4850 y(k)1807 4823
y Fn(;)114 b(X)2029 4838 y Fk(0)2096 4823 y FA(:=)2235
4798 y Fi(e)2227 4823 y Fn(L)2293 4782 y Fm(p)2333 4823
y Fn(;)g(B)33 b FA(:=)28 b Fn(a)2763 4838 y Fm(k)2828
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5023 y Fm(q)p 535 5044 V 535 5101 a Fk(2)609 5067 y FA(and)h
(Assumption)i(4.1)e(applies.)43 b(W)-8 b(e)29 b(v)m(erify)i(the)e
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5468 y Fn(H)1397 5398 y Fh(\000)1463 5371 y Fe(1)p 1462
5383 33 3 v 1462 5424 a Fc(p)1504 5398 y Fm(;q)1389 5496
y(k)1606 5468 y FA(=)1726 5357 y Fi(h)1795 5443 y(e)1773
5468 y Fn(H)1862 5421 y Fh(\000)p Fk(1)p Fm(;q)1854 5496
y(k)2009 5468 y Fn(;)2075 5443 y Fi(e)2053 5468 y Fn(H)2142
5421 y Fk(1)p Fm(;q)2134 5496 y(k)2234 5357 y Fi(i)2291
5506 y Fc(q)r Fg(\000)p Fe(2)p 2291 5522 109 3 v 2315
5563 a(2)p Fc(q)2431 5468 y Fn(:)987 b FA(\(5.5\))p 120
5702 3526 4 v 290 5823 a Fx(Preprin)n(t)26 b(765,)h(W)-7
b(eierstra\031{Institut)26 b(f)1556 5827 y(\177)1554
5823 y(ur)i(Angew)n(andte)f(Analysis)g(und)h(Sto)r(c)n(hastik,)f
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16 17 bop 120 144 a Fr(16)118 b Fs(Hans-Christoph)37
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120 183 3526 4 v 120 383 a FA(According)33 b(to)g([17)o(,)g(4.6.1])f
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554 y Fe(1)p 971 566 33 3 v 971 608 a Fc(p)1013 581 y
Fm(;q)1067 558 y Fg(0)954 679 y Fm(k)1121 652 y Fn(,)-17
b Fl(!)1281 626 y Fi(e)1259 652 y Fn(H)1358 578 y Fe(1)p
1357 590 V 1357 631 a Fc(p)1399 605 y Fm(;q)1453 582
y Fg(0)1507 652 y Fn(,)g Fl(!)1653 626 y Fi(e)1645 652
y Fn(L)1711 610 y Fm(p)1747 587 y Fg(0)1773 652 y Fn(;)2055
612 y Fk(1)p 2054 629 36 4 v 2054 686 a Fm(p)2122 652
y FA(+)2241 612 y Fk(1)p 2230 629 58 4 v 2230 686 a Fm(p)2266
667 y Fg(0)2326 652 y FA(=)2439 612 y Fk(1)p 2439 629
36 4 v 2440 686 a Fm(q)2506 652 y FA(+)2625 612 y Fk(1)p
2614 629 57 4 v 2614 686 a Fm(q)2648 667 y Fg(0)2708
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995 y Fh(\000)2034 968 y Fe(1)p 2032 980 33 3 v 2032
1021 a Fc(p)2074 995 y Fm(;q)1960 1093 y(k)2132 1065
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b(De\014nition)35 b(2.4)g(and)h(De\014nition)f(2.5,)120
1416 y(resp)s(ectiv)m(ely)-8 b(,)37 b(ob)s(ey)e(the)f(resolv)m(en)m(t)j
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b(.)51 b(Lemma)34 b(3.6)120 1560 y(yields)861 1630 y
Fi(\002)911 1686 y(e)903 1711 y Fn(L)969 1670 y Fm(p)1009
1711 y Fn(;)17 b FA(dom)g Fn(A)1327 1726 y Fm(k)1369
1630 y Fi(\003)1411 1750 y Fm(\013)1488 1711 y Fn(,)-17
b Fl(!)1648 1686 y Fi(e)1626 1711 y Fn(H)1715 1664 y
Fk(1)p Fm(;q)1707 1739 y(k)2002 1711 y FA(for)32 b(all)h
Fn(\013)28 b Fl(2)2471 1630 y Fi(\003)2523 1672 y Fk(1)p
2523 1688 36 4 v 2523 1745 a(2)2590 1711 y FA(+)2698
1672 y Fk(1)p 2698 1688 V 2699 1745 a Fm(q)2743 1711
y Fn(;)17 b FA(1)2836 1630 y Fi(\002)2877 1711 y FA(.)541
b(\(5.7\))120 1917 y(\(5.3\))32 b(and)h(\(5.7\))f(imply)691
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2182 y Fm(k)1399 2167 y Fn(A)1472 2182 y Fm(k)1515 2167
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2144 V 2664 2202 a(2)2732 2167 y FA(+)2840 2128 y Fk(1)p
2840 2144 V 2841 2202 a Fm(q)2885 2167 y Fn(;)17 b FA(1[.)413
b(\(5.8\))120 2418 y(No)m(w)38 b(the)h(assertion)f(\(5.4\))f(follo)m
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b(cf.)59 b(Prop)s(osition)38 b(3.5,)120 2562 y(thereb)m(y)c(observing)g
(Theorem)g(5.3.)p 3575 2562 4 66 v 3579 2500 59 4 v 3579
2562 V 3637 2562 4 66 v 120 2798 a Fr(5.5)48 b(De\014nition.)g
FA(Let)42 b Fn(\013)h FA(b)s(e)f(an)g(arbitrary)g(but)g(from)g(no)m(w)h
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y(in)m(terv)-5 b(al)473 2862 y Fi(\003)524 2903 y Fk(1)p
524 2920 36 4 v 524 2977 a(2)592 2943 y FA(+)700 2903
y Fk(1)p 700 2920 V 701 2977 a Fm(q)745 2943 y Fn(;)17
b(\015)845 2862 y Fi(\002)886 2943 y FA(,)33 b(where)i
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f(Assumption)i(4.1.)44 b(Then)34 b(w)m(e)120 3087 y(denote)h(b)m(y)h
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Fa(A)2113 3102 y Fk(1)2153 3087 y Fn(;)17 b(:)g(:)g(:)f(;)h
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f(to)g(the)120 3232 y(domain)1279 3382 y(dom)17 b Fl(A)27
b FA(:=)g([)p Fn(T)1801 3397 y Fk(0)1841 3382 y Fn(;)17
b(T)1942 3397 y Fk(1)1981 3382 y FA(])23 b Fl(\002)f
FA(dom)17 b Fl(A)2411 3341 y Fm(\013)2411 3407 y Fk(0)2460
3382 y Fn(:)120 3588 y FA(Moreo)m(v)m(er,)34 b(w)m(e)g(denote)f(b)m(y)h
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b Fl(A)2823 3552 y Fm(\013)2823 3613 y Fk(0)2905 3588
y FA(in)m(to)3119 3563 y Fi(e)3102 3588 y Fr(H)3190 3552
y Fk(1)p Fm(;q)718 3839 y Fl(k)p Fr(y)r Fl(k)891 3853
y Fd(e)879 3869 y Fb(H)942 3837 y Fe(1)p Fc(;q)942 3890
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3863 y Fk(0)3445 3839 y FA(\(5.9\))120 4102 y(and)33
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4077 y Fi(e)1820 4102 y Fn(H)1909 4066 y Fk(1)p Fm(;q)2033
4102 y FA(in)m(to)2240 4077 y Fi(e)2231 4102 y Fn(L)2297
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Fl(\024)28 b Fn(\025)17 b Fl(k)p Fn( )t Fl(k)1714 4366
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Fe(0)1352 5546 y Fm(;T)1413 5555 y Fe(1)1448 5546 y Fk(])p
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b(e)1669 5460 y Fn(F)1732 5475 y Fm(k)1791 5460 y FA(\()p
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5376 y Fi(\015)2336 5435 y(\015)2407 5483 y Fd(e)2391
5499 y Fm(H)2454 5480 y Fe(1)p Fc(;q)2570 5460 y Fl(\024)2699
5435 y Fi(b)2675 5460 y Fl(F)2747 5475 y Fm(M)2853 5460
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b(eierstra\031{Institut)26 b(f)1556 5827 y(\177)1554
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17 18 bop 120 144 a Fs(Classical)38 b(Solutions)g(of)g(Quasilinear)g(P)
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660 y Fk(2)1400 645 y Fn(;)17 b Fr(y)1503 660 y Fk(2)1565
645 y FA(+)22 b Fr(\010)p FA(\()p Fn(t)1817 660 y Fk(2)1856
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Fl(\024)1790 789 y Fi(b)1776 814 y Fl(E)1829 829 y Fm(M)1924
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839 y Fk(0)2637 814 y Fr(y)2696 829 y Fk(1)2758 814 y
Fl(\000)h(A)2938 773 y Fm(\013)2938 839 y Fk(0)2987 814
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1142 y(e)258 1168 y Fn(F)321 1183 y Fm(k)381 1168 y FA(\()p
Fn(t)454 1183 y Fk(1)493 1168 y Fn(;)17 b Fr(y)596 1183
y Fk(1)658 1168 y FA(+)22 b Fr(\010)p FA(\()p Fn(t)910
1183 y Fk(1)949 1168 y FA(\)\))g Fl(\000)1166 1142 y
Fi(e)1147 1168 y Fn(F)1210 1183 y Fm(k)1269 1168 y FA(\()p
Fn(t)1342 1183 y Fk(2)1382 1168 y Fn(;)17 b Fr(y)1485
1183 y Fk(2)1546 1168 y FA(+)22 b Fr(\010)p FA(\()p Fn(t)1798
1183 y Fk(2)1838 1168 y FA(\)\))1930 1083 y Fi(\015)1930
1143 y(\015)2002 1190 y Fd(e)1986 1207 y Fm(H)2049 1188
y Fe(1)p Fc(;q)1696 1358 y Fl(\024)1825 1332 y Fi(b)1801
1358 y Fl(F)1873 1373 y Fm(M)1968 1277 y Fi(\000)2014
1358 y Fl(j)p Fn(t)2077 1373 y Fk(1)2138 1358 y Fl(\000)h
Fn(t)2273 1373 y Fk(2)2312 1358 y Fl(j)2340 1316 y Fm(\021)2404
1358 y FA(+)f Fl(kA)2632 1316 y Fm(\013)2632 1382 y Fk(0)2681
1358 y Fr(y)2740 1373 y Fk(1)2802 1358 y Fl(\000)g(A)2981
1316 y Fm(\013)2981 1382 y Fk(0)3030 1358 y Fr(y)3089
1373 y Fk(2)3129 1358 y Fl(k)3184 1372 y Fd(e)3179 1388
y Fb(L)3228 1369 y Fc(p)3268 1277 y Fi(\001)3397 1358
y FA(\(5.13\))120 1594 y Fo(for)35 b(al)5 b(l)34 b Fn(k)d
Fl(2)d(f)p FA(1)p Fn(;)17 b(:)g(:)g(:)e(;)i(l)r Fl(g)p
Fo(,)35 b(al)5 b(l)34 b Fn(t)1228 1609 y Fk(1)1268 1594
y Fn(;)f(t)1363 1609 y Fk(2)1431 1594 y Fl(2)28 b FA([)p
Fn(T)1609 1609 y Fk(0)1648 1594 y Fn(;)17 b(T)1749 1609
y Fk(1)1789 1594 y FA(])p Fo(,)35 b(and)f(al)5 b(l)34
b Fr(y)2268 1609 y Fk(1)2308 1594 y Fn(;)f Fr(y)2427
1609 y Fk(2)2495 1594 y Fl(2)28 b Fn(M)10 b Fo(.)120
1858 y(Pr)-5 b(o)g(of.)48 b FA(According)27 b(to)f(Theorem)h(5.4)f(the)
h(set)f Fn(M)37 b FA(is)27 b(not)f(only)g(b)s(ounded)h(in)g(dom)16
b Fl(A)3235 1822 y Fm(\013)3235 1883 y Fk(0)3310 1858
y FA(but)27 b(also)120 2003 y(in)251 1977 y Fi(e)235
2003 y Fr(H)323 1967 y Fk(1)p Fm(;q)416 2003 y FA(.)48
b(Th)m(us,)36 b(b)m(y)f(means)g(of)e(Assumption)j(4.1.i,)e(Lemma)h
(4.11,)f(and)g(Assumption)i(4.1.iv)120 2147 y(w)m(e)e(can)e(estimate)
473 2299 y Fi(\015)473 2359 y(\015)20 b(e)529 2384 y
Fn(E)601 2399 y Fm(k)660 2384 y FA(\()p Fn(t)733 2399
y Fk(1)773 2384 y Fn(;)d Fr(y)876 2399 y Fk(1)937 2384
y FA(+)22 b Fr(\010)p FA(\()p Fn(t)1189 2399 y Fk(1)1229
2384 y FA(\)\))g Fl(\000)1446 2359 y Fi(e)1426 2384 y
Fn(E)1498 2399 y Fm(k)1558 2384 y FA(\()p Fn(t)1631 2399
y Fk(2)1671 2384 y Fn(;)17 b Fr(y)1774 2399 y Fk(2)1835
2384 y FA(+)22 b Fr(\010)p FA(\()p Fn(t)2087 2399 y Fk(2)2127
2384 y FA(\))o(\))2219 2299 y Fi(\015)2219 2359 y(\015)2281
2406 y Fd(e)2274 2423 y Fm(L)2322 2404 y Fg(1)556 2553
y Fl(\024)84 b(E)770 2568 y Fm(M)865 2473 y Fi(\000)911
2553 y Fl(j)p Fn(t)974 2568 y Fk(1)1035 2553 y Fl(\000)23
b Fn(t)1170 2568 y Fk(2)1210 2553 y Fl(j)1238 2512 y
Fm(\021)1301 2553 y FA(+)f Fl(k)p Fr(y)1508 2568 y Fk(1)1570
2553 y FA(+)g Fr(\010)p FA(\()p Fn(t)1822 2568 y Fk(1)1861
2553 y FA(\))g Fl(\000)h Fr(y)2080 2568 y Fk(2)2142 2553
y Fl(\000)f Fr(\010)p FA(\()p Fn(t)2395 2568 y Fk(2)2435
2553 y FA(\))p Fl(k)2535 2567 y Fd(e)2523 2584 y Fb(H)2586
2565 y Fe(1)p Fc(;q)2674 2473 y Fi(\001)556 2736 y Fl(\024)84
b(E)770 2751 y Fm(M)865 2625 y Fi(\020)925 2736 y Fl(j)p
Fn(t)988 2751 y Fk(1)1049 2736 y Fl(\000)23 b Fn(t)1184
2751 y Fk(2)1223 2736 y Fl(j)1251 2695 y Fm(\021)1315
2736 y FA(+)f Fl(k)p Fr(\010)p Fl(k)1594 2767 y Fm(C)1649
2748 y Fc(\021)1687 2767 y Fk(\([)p Fm(T)1775 2776 y
Fe(0)1809 2767 y Fm(;T)1870 2776 y Fe(1)1905 2767 y Fk(];)1956
2750 y Fd(e)1945 2767 y Fb(H)2008 2748 y Fe(1)p Fc(;q)2091
2767 y Fk(\))2123 2736 y Fl(j)p Fn(t)2186 2751 y Fk(1)2247
2736 y Fl(\000)h Fn(t)2382 2751 y Fk(2)2421 2736 y Fl(j)2449
2695 y Fm(\021)2513 2736 y FA(+)f Fl(k)p Fr(y)2720 2751
y Fk(1)2782 2736 y Fl(\000)g Fr(y)2940 2751 y Fk(2)2980
2736 y Fl(k)3042 2750 y Fd(e)3030 2767 y Fb(H)3093 2748
y Fe(1)p Fc(;q)3181 2625 y Fi(\021)556 2949 y Fl(\024)84
b(E)770 2964 y Fm(M)865 2838 y Fi(\020)925 2949 y FA(\(1)21
b(+)h Fl(k)p Fr(\010)p Fl(k)1312 2979 y Fm(C)1367 2960
y Fc(\021)1405 2979 y Fk(\([)p Fm(T)1493 2988 y Fe(0)1528
2979 y Fm(;T)1589 2988 y Fe(1)1623 2979 y Fk(];)1674
2962 y Fd(e)1663 2979 y Fb(H)1726 2960 y Fe(1)p Fc(;q)1809
2979 y Fk(\))1841 2949 y FA(\))p Fl(j)p Fn(t)1942 2964
y Fk(1)2003 2949 y Fl(\000)h Fn(t)2138 2964 y Fk(2)2178
2949 y Fl(j)2206 2907 y Fm(\021)2269 2949 y FA(+)f Fn(\024)p
Fl(kA)2553 2907 y Fm(\013)2553 2973 y Fk(0)2602 2949
y Fr(y)2661 2964 y Fk(1)2723 2949 y Fl(\000)h(A)2903
2907 y Fm(\013)2903 2973 y Fk(0)2952 2949 y Fr(y)3011
2964 y Fk(2)3050 2949 y Fl(k)3105 2963 y Fd(e)3100 2979
y Fb(L)3149 2960 y Fc(p)3189 2838 y Fi(\021)3265 2949
y Fn(:)120 3185 y FA(This)48 b(pro)m(v)m(es)g(\(5.12\))o(.)86
b(In)47 b(order)f(to)g(sho)m(w)j(\(5.13\))d(w)m(e)i(estimate)g(b)m(y)f
(means)h(of)e(Assump-)120 3330 y(tion)33 b(4.1.ii,)f(Lemma)h(4.11,)f
(and)h(Assumption)h(4.1.iv:)464 3482 y Fi(\015)464 3541
y(\015)19 b(e)519 3566 y Fn(F)582 3581 y Fm(k)642 3566
y FA(\()p Fn(t)715 3581 y Fk(1)754 3566 y Fn(;)e Fr(y)857
3581 y Fk(1)919 3566 y FA(+)22 b Fr(\010)p FA(\()p Fn(t)1171
3581 y Fk(1)1210 3566 y FA(\)\))g Fl(\000)1427 3541 y
Fi(e)1408 3566 y Fn(F)1471 3581 y Fm(k)1530 3566 y FA(\()p
Fn(t)1603 3581 y Fk(2)1643 3566 y Fn(;)17 b Fr(y)1746
3581 y Fk(2)1807 3566 y FA(+)22 b Fr(\010)p FA(\()p Fn(t)2059
3581 y Fk(2)2099 3566 y FA(\)\))2191 3482 y Fi(\015)2191
3541 y(\015)2263 3589 y Fd(e)2247 3605 y Fm(H)2310 3586
y Fe(1)p Fc(;q)547 3736 y Fl(\024)83 b(F)779 3751 y Fm(M)875
3655 y Fi(\000)920 3736 y Fl(j)p Fn(t)983 3751 y Fk(1)1045
3736 y Fl(\000)22 b Fn(t)1179 3751 y Fk(2)1219 3736 y
Fl(j)1247 3695 y Fm(\021)1311 3736 y FA(+)g Fl(k)p Fr(y)1518
3751 y Fk(1)1579 3736 y FA(+)g Fr(\010)p FA(\()p Fn(t)1831
3751 y Fk(1)1871 3736 y FA(\))g Fl(\000)h Fr(y)2090 3751
y Fk(2)2151 3736 y Fl(\000)g Fr(\010)p FA(\()p Fn(t)2405
3751 y Fk(2)2445 3736 y FA(\))p Fl(k)2545 3750 y Fd(e)2533
3766 y Fb(H)2596 3747 y Fe(1)p Fc(;q)2684 3655 y Fi(\001)547
3918 y Fl(\024)83 b(F)779 3933 y Fm(M)875 3808 y Fi(\020)934
3918 y Fl(j)p Fn(t)997 3933 y Fk(1)1059 3918 y Fl(\000)22
b Fn(t)1193 3933 y Fk(2)1233 3918 y Fl(j)1261 3877 y
Fm(\021)1325 3918 y FA(+)g Fl(k)p Fr(\010)p Fl(k)1604
3949 y Fm(C)1659 3930 y Fc(\021)1696 3949 y Fk(\([)p
Fm(T)1784 3958 y Fe(0)1819 3949 y Fm(;T)1880 3958 y Fe(1)1914
3949 y Fk(];)1966 3932 y Fd(e)1954 3949 y Fb(H)2017 3930
y Fe(1)p Fc(;q)2101 3949 y Fk(\))2132 3918 y Fl(j)p Fn(t)2195
3933 y Fk(1)2257 3918 y Fl(\000)g Fn(t)2391 3933 y Fk(2)2431
3918 y Fl(j)2459 3877 y Fm(\021)2523 3918 y FA(+)g Fl(k)p
Fr(y)2730 3933 y Fk(1)2791 3918 y Fl(\000)h Fr(y)2950
3933 y Fk(2)2989 3918 y Fl(k)3051 3932 y Fd(e)3039 3949
y Fb(H)3102 3930 y Fe(1)p Fc(;q)3191 3808 y Fi(\021)547
4131 y Fl(\024)83 b(F)779 4146 y Fm(M)875 4020 y Fi(\020)934
4131 y FA(\(1)22 b(+)g Fl(k)p Fr(\010)p Fl(k)1322 4161
y Fm(C)1377 4143 y Fc(\021)1415 4161 y Fk(\([)p Fm(T)1503
4170 y Fe(0)1537 4161 y Fm(;T)1598 4170 y Fe(1)1633 4161
y Fk(];)1684 4144 y Fd(e)1673 4161 y Fb(H)1736 4143 y
Fe(1)p Fc(;q)1819 4161 y Fk(\))1851 4131 y FA(\))p Fl(j)p
Fn(t)1952 4146 y Fk(1)2013 4131 y Fl(\000)h Fn(t)2148
4146 y Fk(2)2187 4131 y Fl(j)2215 4090 y Fm(\021)2279
4131 y FA(+)f Fn(\024)p Fl(kA)2563 4090 y Fm(\013)2563
4155 y Fk(0)2612 4131 y Fr(y)2671 4146 y Fk(1)2733 4131
y Fl(\000)g(A)2912 4090 y Fm(\013)2912 4155 y Fk(0)2961
4131 y Fr(y)3020 4146 y Fk(2)3060 4131 y Fl(k)3115 4145
y Fd(e)3110 4161 y Fb(L)3159 4143 y Fc(p)3199 4020 y
Fi(\021)3275 4131 y Fn(:)120 4367 y FA(\(5.11\))32 b(follo)m(ws)h(from)
f(\(5.12\))g(and)h(\(5.13\))o(.)p 3575 4367 4 66 v 3579
4305 59 4 v 3579 4367 V 3637 4367 4 66 v 120 4589 a Fr(5.8)39
b(Theorem.)k Fo(The)35 b(op)-5 b(er)g(ator)36 b Fl(A)g
Fo(fr)-5 b(om)35 b(De\014nition)g(5.5)g(satis\014es)44
b FA(\(3.10\))35 b Fo(with)h(r)-5 b(esp)g(e)g(ct)36 b(to)120
4733 y(the)f(Banach)e(sp)-5 b(ac)g(e)34 b Fn(X)i FA(:=)1142
4708 y Fi(e)1136 4733 y Fr(L)1203 4697 y Fm(p)1243 4733
y Fo(.)120 4997 y(Pr)-5 b(o)g(of.)48 b FA(F)-8 b(or)28
b(an)h(arbitrary)f Fn(R)h(>)e FA(0)i(w)m(e)g(regard)g(the)g(ball)f
Fn(B)2284 5012 y Fm(R)2371 4997 y FA(with)h(radius)g
Fn(R)g FA(in)g(the)g(space)3518 4972 y Fi(e)3512 4997
y Fr(L)3579 4961 y Fm(p)3619 4997 y FA(.)120 5142 y(Then)i(the)g(set)g
Fl(A)768 5101 y Fh(\000)p Fm(\013)768 5166 y Fk(0)871
5142 y Fn(B)945 5157 y Fm(R)1033 5142 y FA(is)g(iden)m(tical)g(with)g
(the)f Fn(R)q FA({ball)g(in)h(dom)17 b Fl(A)2608 5106
y Fm(\013)2608 5166 y Fk(0)2657 5142 y FA(;)31 b(hence,)h(it)e(is)g(a)g
(b)s(ounded)120 5286 y(set)j(in)402 5261 y Fi(e)386 5286
y Fr(H)474 5250 y Fk(1)p Fm(;q)567 5286 y FA(,)f(cf.)44
b(Theorem)34 b(5.4.)43 b(Let)1175 5523 y Fn(t)1210 5538
y Fk(1)1250 5523 y Fn(;)33 b(t)1345 5538 y Fk(2)1412
5523 y Fl(2)28 b FA([)p Fn(T)1590 5538 y Fk(0)1630 5523
y Fn(;)17 b(T)1731 5538 y Fk(1)1770 5523 y FA(])p Fn(;)212
b Fr(w)2117 5538 y Fk(1)2157 5523 y Fn(;)33 b Fr(w)2298
5538 y Fk(2)2365 5523 y Fl(2)28 b Fn(B)2533 5538 y Fm(R)3397
5523 y FA(\(5.14\))p 120 5702 3526 4 v 290 5823 a Fx(Preprin)n(t)e
(765,)h(W)-7 b(eierstra\031{Institut)26 b(f)1556 5827
y(\177)1554 5823 y(ur)i(Angew)n(andte)f(Analysis)g(und)h(Sto)r(c)n
(hastik,)f(Berlin)g(2002)p eop
%%Page: 18 20
18 19 bop 120 144 a Fr(18)118 b Fs(Hans-Christoph)37
b(Kaiser,)g(Ha)n(gen)g(Neidhardt,)h(and)g(Jo)n(a)n(chim)h(Rehber)n(g)p
120 183 3526 4 v 120 383 a FA(b)s(e)33 b(arbitrarily)g(c)m(hosen.)45
b(W)-8 b(e)33 b(abbreviate)311 601 y Fr(y)370 616 y Fm(j)435
601 y FA(=)538 520 y Fi(\000)584 601 y Fn(y)636 554 y
Fm(j)632 629 y(k)674 520 y Fi(\001)720 640 y Fm(k)r Fh(2f)p
Fk(1)p Fm(;:::)n(;l)q Fh(g)1063 601 y FA(:=)28 b Fl(A)1274
560 y Fh(\000)p Fm(\013)1274 626 y Fk(0)1378 601 y Fr(w)1459
616 y Fm(j)1495 601 y Fn(;)1727 576 y Fi(e)1707 601 y
Fn(E)1785 554 y Fm(j)1779 629 y(k)1850 601 y FA(:=)2000
576 y Fi(e)1981 601 y Fn(E)2053 616 y Fm(k)2112 601 y
FA(\()p Fn(t)2185 616 y Fm(j)2222 601 y Fn(;)17 b Fr(y)2325
616 y Fm(j)2383 601 y FA(+)22 b Fr(\010)p FA(\()p Fn(t)2635
616 y Fm(j)2672 601 y FA(\)\))16 b Fn(;)313 766 y Fi(e)294
791 y Fn(F)371 744 y Fm(j)357 819 y(k)435 791 y FA(:=)584
766 y Fi(e)565 791 y Fn(F)628 806 y Fm(k)688 791 y FA(\()p
Fn(t)761 806 y Fm(j)798 791 y Fn(;)h Fr(y)901 806 y Fm(j)959
791 y FA(+)22 b Fr(\010)p FA(\()p Fn(t)1211 806 y Fm(j)1248
791 y FA(\)\))16 b Fn(;)1722 766 y Fi(e)1703 791 y Fn(G)1780
744 y Fm(j)1780 819 y(k)1850 791 y FA(:=)2000 766 y Fi(e)1981
791 y Fn(G)2058 806 y Fm(k)2117 791 y FA(\()p Fn(t)2190
806 y Fm(j)2227 791 y Fn(;)h Fr(y)2330 806 y Fm(j)2388
791 y FA(+)22 b Fr(\010)p FA(\()p Fn(t)2640 806 y Fm(j)2677
791 y FA(\)\))16 b Fn(;)2894 692 y(j)33 b FA(=)28 b(1)p
Fn(;)17 b FA(2)p Fn(:)157 b FA(\(5.15\))120 1017 y(Then)42
b(the)g Fn(k)s FA({th)f(comp)s(onen)m(t)h(of)1422 936
y Fi(\000)1468 1017 y Fl(A)p FA(\()p Fn(t)1621 1032 y
Fk(1)1660 1017 y Fn(;)17 b Fr(y)1763 1032 y Fk(1)1802
1017 y FA(\))28 b Fl(\000)g(A)p FA(\()p Fn(t)2126 1032
y Fk(2)2166 1017 y Fn(;)17 b Fr(y)2269 1032 y Fk(2)2308
1017 y FA(\))2346 936 y Fi(\001)2391 1017 y Fl(A)2471
975 y Fh(\000)p Fk(1)2471 1041 y(0)2606 1017 y FA(can)42
b(b)s(e)f(estimated)h(in)f(the)120 1161 y(follo)m(wing)33
b(w)m(a)m(y)744 1310 y Fi(\015)744 1370 y(\015)799 1314
y(\000)845 1395 y FA(\(1)22 b(+)1071 1370 y Fi(e)1052
1395 y Fn(E)1130 1354 y Fk(1)1124 1419 y Fm(k)1188 1370
y Fi(e)1169 1395 y Fn(F)1246 1354 y Fk(1)1232 1419 y
Fm(k)1286 1395 y Fn(A)1359 1410 y Fm(k)1401 1395 y FA(\))g
Fl(\000)h FA(\(1)f(+)1787 1370 y Fi(e)1768 1395 y Fn(E)1846
1354 y Fk(2)1840 1419 y Fm(k)1904 1370 y Fi(e)1885 1395
y Fn(F)1962 1354 y Fk(2)1948 1419 y Fm(k)2002 1395 y
Fn(A)2075 1410 y Fm(k)2117 1395 y FA(\))2155 1314 y Fi(\001)2201
1395 y FA(\(1)g(+)g Fn(U)2474 1410 y Fm(k)2517 1395 y
Fn(A)2590 1410 y Fm(k)2632 1395 y FA(\))2670 1354 y Fh(\000)p
Fk(1)2765 1310 y Fi(\015)2765 1370 y(\015)2820 1434 y
Fh(B)r Fk(\()2901 1417 y Fd(e)2895 1434 y Fm(L)2943 1415
y Fc(p)2980 1434 y Fk(\))827 1658 y Fl(\024)988 1484
y Fi(\015)988 1543 y(\015)988 1603 y(\015)988 1663 y(\015)988
1723 y(\015)1072 1565 y(e)1053 1591 y Fn(E)1131 1554
y Fk(1)1125 1617 y Fm(k)1189 1565 y Fi(e)1170 1591 y
Fn(F)1247 1554 y Fk(1)1233 1617 y Fm(k)1309 1591 y Fl(\000)1428
1565 y Fi(e)1408 1591 y Fn(E)1486 1554 y Fk(2)1480 1617
y Fm(k)1545 1565 y Fi(e)1526 1591 y Fn(F)1603 1554 y
Fk(2)1589 1617 y Fm(k)p 1053 1635 590 4 v 1293 1726 a
Fn(U)1359 1741 y Fm(k)1652 1484 y Fi(\015)1652 1543 y(\015)1652
1603 y(\015)1652 1663 y(\015)1652 1723 y(\015)1707 1787
y Fh(B)r Fk(\()1788 1770 y Fd(e)1782 1787 y Fm(L)1830
1768 y Fc(p)1867 1787 y Fk(\))1915 1573 y Fi(\015)1915
1633 y(\015)1970 1658 y Fn(U)2036 1673 y Fm(k)2079 1658
y Fn(A)2152 1673 y Fm(k)2195 1658 y FA(\(1)g(+)g Fn(U)2468
1673 y Fm(k)2511 1658 y Fn(A)2584 1673 y Fm(k)2627 1658
y FA(\))2665 1617 y Fh(\000)p Fk(1)2759 1573 y Fi(\015)2759
1633 y(\015)2814 1697 y Fh(B)r Fk(\()2895 1680 y Fd(e)2889
1697 y Fm(L)2937 1678 y Fc(p)2974 1697 y Fk(\))827 2011
y Fl(\024)988 1837 y Fi(\015)988 1896 y(\015)988 1956
y(\015)988 2016 y(\015)988 2076 y(\015)1072 1918 y(e)1053
1943 y Fn(E)1131 1907 y Fk(1)1125 1969 y Fm(k)1189 1918
y Fi(e)1170 1943 y Fn(F)1247 1907 y Fk(1)1233 1969 y
Fm(k)1309 1943 y Fl(\000)1428 1918 y Fi(e)1408 1943 y
Fn(E)1486 1907 y Fk(2)1480 1969 y Fm(k)1545 1918 y Fi(e)1526
1943 y Fn(F)1603 1907 y Fk(2)1589 1969 y Fm(k)p 1053
1988 V 1293 2079 a Fn(U)1359 2094 y Fm(k)1652 1837 y
Fi(\015)1652 1896 y(\015)1652 1956 y(\015)1652 2016 y(\015)1652
2076 y(\015)1707 2140 y Fm(L)1755 2121 y Fg(1)1841 1900
y Fi(\020)1900 2011 y FA(1)g(+)2069 1926 y Fi(\015)2069
1986 y(\015)2125 2011 y FA(\(1)g(+)g Fn(U)2398 2026 y
Fm(k)2441 2011 y Fn(A)2514 2026 y Fm(k)2556 2011 y FA(\))2594
1970 y Fh(\000)p Fk(1)2689 1926 y Fi(\015)2689 1986 y(\015)2744
2050 y Fh(B)r Fk(\()2825 2033 y Fd(e)2819 2050 y Fm(L)2867
2031 y Fc(p)2903 2050 y Fk(\))2935 1900 y Fi(\021)828
2352 y FA(=)988 2267 y Fi(\015)988 2327 y(\015)d(e)1043
2352 y Fn(E)1121 2311 y Fk(1)1115 2377 y Fm(k)1179 2327
y Fi(e)1160 2352 y Fn(F)1237 2311 y Fk(1)1223 2377 y
Fm(k)1299 2352 y Fl(\000)1418 2327 y Fi(e)1398 2352 y
Fn(E)1476 2311 y Fk(2)1470 2377 y Fm(k)1535 2327 y Fi(e)1516
2352 y Fn(F)1593 2311 y Fk(2)1579 2377 y Fm(k)1632 2267
y Fi(\015)1632 2327 y(\015)1687 2391 y Fm(L)1735 2372
y Fg(1)1814 2257 y FA(1)j(+)1983 2173 y Fi(\015)1983
2233 y(\015)2039 2257 y FA(\(1)g(+)g Fn(U)2312 2272 y
Fm(k)2354 2257 y Fn(A)2427 2272 y Fm(k)2470 2257 y FA(\))2508
2221 y Fh(\000)p Fk(1)2603 2173 y Fi(\015)2603 2233 y(\015)2658
2296 y Fh(B)r Fk(\()2739 2280 y Fd(e)2733 2296 y Fm(L)2781
2278 y Fc(p)2817 2296 y Fk(\))p 1814 2329 1035 4 v 1968
2420 a FA(vraimin)2296 2435 y Fm(x)p Fh(2)p Fk(\012)2455
2420 y Fn(U)2521 2435 y Fm(k)2564 2420 y FA(\()p Fn(x)p
FA(\))2859 2352 y Fn(:)120 2612 y FA(The)35 b(last)g(fraction)f(is)h
(\014nite)g(according)g(to)f(Assumption)i(4.1)e(and)h(Prop)s(osition)g
(3.4.)48 b(Th)m(us,)120 2756 y(it)33 b(remains)g(to)f(estimate)i(b)m(y)
g(means)f(of)f(Lemma)i(5.7)e(and)g(\(5.10\))331 2905
y Fi(\015)331 2965 y(\015)20 b(e)387 2990 y Fn(E)465
2949 y Fk(1)459 3015 y Fm(k)523 2965 y Fi(e)504 2990
y Fn(F)581 2949 y Fk(1)567 3015 y Fm(k)642 2990 y Fl(\000)762
2965 y Fi(e)742 2990 y Fn(E)820 2949 y Fk(2)814 3015
y Fm(k)878 2965 y Fi(e)860 2990 y Fn(F)937 2949 y Fk(2)923
3015 y Fm(k)976 2905 y Fi(\015)976 2965 y(\015)1031 3029
y Fm(L)1079 3010 y Fg(1)3397 2990 y FA(\(5.16\))414 3160
y Fl(\024)575 3075 y Fi(\015)575 3135 y(\015)630 3079
y(\000)695 3134 y(e)676 3160 y Fn(E)748 3175 y Fm(k)807
3160 y FA(\()p Fn(t)880 3175 y Fk(1)920 3160 y Fn(;)d
Fr(y)1023 3175 y Fk(1)1084 3160 y FA(+)22 b Fr(\010)p
FA(\()p Fn(t)1336 3175 y Fk(1)1376 3160 y FA(\)\))g Fl(\000)1593
3134 y Fi(e)1574 3160 y Fn(E)1646 3175 y Fm(k)1705 3160
y FA(\()p Fn(t)1778 3175 y Fk(2)1818 3160 y Fn(;)17 b
Fr(y)1921 3175 y Fk(2)1982 3160 y FA(+)22 b Fr(\010)p
FA(\()p Fn(t)2234 3175 y Fk(2)2274 3160 y FA(\)\))2366
3079 y Fi(\001)2431 3134 y(e)2412 3160 y Fn(F)2475 3175
y Fm(k)2534 3160 y FA(\()p Fn(t)2607 3175 y Fk(1)2647
3160 y Fn(;)17 b Fr(y)2750 3175 y Fk(1)2811 3160 y FA(+)22
b Fr(\010)p FA(\()p Fn(t)3063 3175 y Fk(1)3103 3160 y
FA(\)\))3195 3075 y Fi(\015)3195 3135 y(\015)3251 3199
y Fm(L)3299 3180 y Fg(1)575 3329 y FA(+)651 3244 y Fi(\015)651
3304 y(\015)e(e)706 3329 y Fn(E)778 3344 y Fm(k)838 3329
y FA(\()p Fn(t)911 3344 y Fk(2)950 3329 y Fn(;)d Fr(y)1053
3344 y Fk(2)1115 3329 y FA(+)22 b Fr(\010)p FA(\()p Fn(t)1367
3344 y Fk(2)1406 3329 y FA(\)\))1499 3248 y Fi(\000)1563
3304 y(e)1544 3329 y Fn(F)1607 3344 y Fm(k)1667 3329
y FA(\()p Fn(t)1740 3344 y Fk(1)1779 3329 y Fn(;)17 b
Fr(y)1882 3344 y Fk(1)1944 3329 y FA(+)22 b Fr(\010)p
FA(\()p Fn(t)2196 3344 y Fk(1)2235 3329 y FA(\)\))g Fl(\000)2452
3304 y Fi(e)2433 3329 y Fn(F)2496 3344 y Fm(k)2555 3329
y FA(\()p Fn(t)2628 3344 y Fk(2)2668 3329 y Fn(;)17 b
Fr(y)2771 3344 y Fk(2)2832 3329 y FA(+)22 b Fr(\010)p
FA(\()p Fn(t)3084 3344 y Fk(2)3124 3329 y FA(\)\))3216
3248 y Fi(\001)3262 3244 y(\015)3262 3304 y(\015)3317
3368 y Fm(L)3365 3349 y Fg(1)414 3498 y Fl(\024)84 b
FA(2)17 b Fn(\025)728 3473 y Fi(b)715 3498 y Fl(E)768
3526 y Fh(A)824 3496 y Fg(\000)p Fc(\013)824 3547 y Fe(0)915
3526 y Fm(B)968 3537 y Fc(R)1047 3473 y Fi(b)1023 3498
y Fl(F)1095 3526 y Fh(A)1151 3496 y Fg(\000)p Fc(\013)1151
3547 y Fe(0)1243 3526 y Fm(B)1296 3537 y Fc(R)1367 3418
y Fi(\000)1413 3498 y Fl(j)p Fn(t)1476 3513 y Fk(1)1537
3498 y Fl(\000)23 b Fn(t)1672 3513 y Fk(2)1711 3498 y
Fl(j)1739 3457 y Fm(\021)1803 3498 y FA(+)f Fl(k)p Fr(w)2032
3513 y Fk(1)2094 3498 y Fl(\000)g Fr(w)2274 3513 y Fk(2)2314
3498 y Fl(k)2369 3512 y Fd(e)2364 3529 y Fb(L)2413 3510
y Fc(p)2453 3418 y Fi(\001)2515 3498 y Fn(:)p 3575 3732
4 66 v 3579 3669 59 4 v 3579 3732 V 3637 3732 4 66 v
120 3995 a FA(In)31 b(order)g(to)g(apply)g(Sob)s(olevskii's)j(Prop)s
(osition)d(3.7)f(to)h(the)g(Problem)h(4.12)e(w)m(e)i(still)g(ha)m(v)m
(e)g(to)120 4140 y(pro)m(v)m(e)i(that)e(the)h(righ)m(t)g(hand)g(side)g
(of)40 b(\(4.12\))31 b(satis\014es)k(\(3.11\))o(.)120
4359 y Fr(5.9)44 b(Theorem.)h Fo(Each)39 b Fn(f)1118
4374 y Fm(k)1200 4359 y Fo(fr)-5 b(om)47 b FA(\(4.13\))39
b Fo(pr)-5 b(ovides)38 b(a)i(mapping)e(fr)-5 b(om)39
b FA([)p Fn(T)2923 4374 y Fk(0)2963 4359 y Fn(;)17 b(T)3064
4374 y Fk(1)3103 4359 y FA(])26 b Fl(\002)3275 4333 y
Fi(e)3259 4359 y Fr(H)3347 4322 y Fk(1)p Fm(;q)3479 4359
y Fo(into)128 4478 y Fi(e)120 4503 y Fn(L)186 4467 y
Fm(p)226 4503 y Fo(.)44 b(Mor)-5 b(e)g(over,)34 b(if)f
Fn(B)925 4518 y Fm(R)1016 4503 y Fo(is)g(again)g(the)g(b)-5
b(al)5 b(l)33 b(with)g(r)-5 b(adius)33 b Fn(R)i Fo(in)2456
4478 y Fi(e)2448 4503 y Fn(L)2514 4467 y Fm(p)2554 4503
y Fo(,)e(and)g Fr(f)44 b Fo(denotes)33 b(the)g(ve)-5
b(ctor)120 4647 y FA(\()p Fn(f)206 4662 y Fk(1)245 4647
y Fn(;)17 b(:)g(:)g(:)f(;)h(f)512 4662 y Fm(l)538 4647
y FA(\))p Fo(,)35 b(then)f(for)h(e)-5 b(ach)34 b Fn(R)29
b(>)f FA(0)34 b Fo(ther)-5 b(e)35 b(is)g(a)f(c)-5 b(onstant)35
b Fn(C)2413 4662 y Fm(R)2505 4647 y Fo(such)g(that)351
4796 y Fi(\015)351 4856 y(\015)406 4881 y Fr(f)10 b FA(\()p
Fn(t)523 4896 y Fk(1)563 4881 y Fn(;)17 b Fl(A)687 4840
y Fh(\000)p Fm(\013)687 4906 y Fk(0)791 4881 y Fr(w)872
4896 y Fk(1)911 4881 y FA(\))22 b Fl(\000)h Fr(f)10 b
FA(\()p Fn(t)1188 4896 y Fk(2)1228 4881 y Fn(;)17 b Fl(A)1352
4840 y Fh(\000)p Fm(\013)1352 4906 y Fk(0)1455 4881 y
Fr(w)1536 4896 y Fk(2)1576 4881 y FA(\))1614 4796 y Fi(\015)1614
4856 y(\015)1674 4903 y Fd(e)1669 4920 y Fb(L)1718 4901
y Fc(p)1786 4881 y Fl(\024)28 b Fn(C)1961 4896 y Fm(R)2035
4800 y Fi(\000)2081 4881 y Fl(j)p Fn(t)2144 4896 y Fk(1)2205
4881 y Fl(\000)23 b Fn(t)2340 4896 y Fk(2)2379 4881 y
Fl(j)2407 4840 y Fm(\021)2471 4881 y FA(+)f Fl(k)p Fr(w)2700
4896 y Fk(1)2762 4881 y Fl(\000)g Fr(w)2942 4896 y Fk(2)2982
4881 y Fl(k)3037 4895 y Fd(e)3032 4912 y Fb(L)3081 4893
y Fc(p)3120 4800 y Fi(\001)3397 4881 y FA(\(5.17\))120
5115 y Fo(for)35 b(al)5 b(l)34 b Fn(t)450 5130 y Fk(1)490
5115 y Fo(,)h Fn(t)590 5130 y Fk(2)657 5115 y Fl(2)28
b FA([)p Fn(T)835 5130 y Fk(0)875 5115 y Fn(;)17 b(T)976
5130 y Fk(1)1015 5115 y FA(])35 b Fo(and)f(al)5 b(l)35
b Fr(w)1487 5130 y Fk(1)1526 5115 y Fo(,)g Fr(w)1672
5130 y Fk(2)1739 5115 y Fl(2)28 b Fn(B)1907 5130 y Fm(R)1965
5115 y Fo(.)120 5378 y(Pr)-5 b(o)g(of.)48 b FA(The)40
b(\014rst)f(assertion)h(immediately)h(follo)m(ws)e(from)f(Assumption)j
(4.1.)61 b(W)-8 b(e)40 b(supp)s(ose)120 5523 y Fn(t)155
5538 y Fk(1)195 5523 y FA(,)d Fn(t)294 5538 y Fk(2)367
5523 y Fl(2)e FA([)p Fn(T)552 5538 y Fk(0)591 5523 y
Fn(;)17 b(T)692 5538 y Fk(1)732 5523 y FA(])36 b(and)g
Fr(w)1069 5538 y Fk(1)1109 5523 y FA(,)h Fr(w)1254 5538
y Fk(2)1327 5523 y Fl(2)e Fn(B)1502 5538 y Fm(R)1596
5523 y FA(to)g(b)s(e)i(arbitrarily)f(c)m(hosen)i(and)f(adopt)f(the)g
(notation)p 120 5702 3526 4 v 290 5823 a Fx(Preprin)n(t)26
b(765,)h(W)-7 b(eierstra\031{Institut)26 b(f)1556 5827
y(\177)1554 5823 y(ur)i(Angew)n(andte)f(Analysis)g(und)h(Sto)r(c)n
(hastik,)f(Berlin)g(2002)p eop
%%Page: 19 21
19 20 bop 120 144 a Fs(Classical)38 b(Solutions)g(of)g(Quasilinear)g(P)
-9 b(arabolic)38 b(Systems)618 b Fr(19)p 120 183 3526
4 v 120 383 a FA(\(5.15\))o(.)43 b(As)30 b(in)g(the)g(pro)s(of)e(of)h
(Theorem)i(5.8)e(one)h(obtains)g(that)g Fl(A)2582 342
y Fh(\000)p Fm(\013)2582 407 y Fk(0)2685 383 y Fn(B)2759
398 y Fm(R)2847 383 y FA(is)g(a)f(b)s(ounded)h(set)h(in)136
502 y Fi(e)120 527 y Fr(H)208 491 y Fk(1)p Fm(;q)301
527 y FA(;)j Fl(A)442 486 y Fh(\000)p Fm(\013)442 552
y Fk(0)546 527 y Fn(B)620 542 y Fm(R)712 527 y FA(is)g(con)m(tained)h
(in)f(the)g Fn(\024R)h FA(ball)f(of)2023 502 y Fi(e)2007
527 y Fr(H)2095 491 y Fk(1)p Fm(;q)2187 527 y FA(,)g(cf.)48
b(\(5.9\))o(.)g(F)-8 b(or)33 b(eac)m(h)i Fn(k)e Fl(2)d(f)p
FA(1)p Fn(;)17 b(:)g(:)g(:)e(;)i(l)r Fl(g)120 672 y FA(there)33
b(is)336 788 y Fi(\015)336 848 y(\015)391 873 y Fn(f)439
888 y Fm(k)482 873 y FA(\()p Fn(t)555 888 y Fk(1)595
873 y Fn(;)17 b Fr(y)698 888 y Fk(1)737 873 y FA(\))22
b Fl(\000)h Fn(f)945 888 y Fm(k)987 873 y FA(\()p Fn(t)1060
888 y Fk(2)1100 873 y Fn(;)17 b Fr(y)1203 888 y Fk(2)1242
873 y FA(\))1280 788 y Fi(\015)1280 848 y(\015)1342 895
y Fd(e)1336 912 y Fm(L)1384 893 y Fc(p)1452 873 y Fl(\024)1557
729 y Fi(\015)1557 788 y(\015)1557 848 y(\015)1557 908
y(\015)1622 806 y Fn(@)5 b FA(\010)1748 821 y Fm(k)p
1622 850 171 4 v 1661 941 a Fn(@)g(t)1802 873 y FA(\()p
Fn(t)1875 888 y Fk(1)1915 873 y FA(\))22 b Fl(\000)2084
806 y Fn(@)5 b FA(\010)2210 821 y Fm(k)p 2084 850 V 2123
941 a Fn(@)g(t)2264 873 y FA(\()p Fn(t)2337 888 y Fk(2)2377
873 y FA(\))2415 729 y Fi(\015)2415 788 y(\015)2415 848
y(\015)2415 908 y(\015)2477 955 y Fd(e)2470 972 y Fm(L)2518
953 y Fc(p)2581 873 y FA(+)2679 788 y Fi(\015)2679 848
y(\015)2734 873 y Fn(y)2786 832 y Fk(1)2782 898 y Fm(k)2847
873 y Fl(\000)22 b Fn(y)2998 832 y Fk(2)2994 898 y Fm(k)3037
788 y Fi(\015)3037 848 y(\015)3099 895 y Fd(e)3092 912
y Fm(L)3140 893 y Fc(p)3397 873 y FA(\(5.18\))542 1120
y(+)640 1005 y Fi(\015)640 1065 y(\015)640 1125 y(\015)715
1094 y(e)696 1120 y Fn(E)774 1078 y Fk(1)768 1144 y Fm(k)830
1009 y Fi(D)891 1120 y Fl(r)992 1094 y Fi(e)974 1120
y Fn(F)1051 1078 y Fk(1)1037 1144 y Fm(k)1090 1120 y
Fn(;)17 b(\026)1193 1135 y Fm(k)1235 1120 y Fl(r)p Fn(y)1370
1078 y Fk(1)1366 1144 y Fm(k)1408 1009 y Fi(E)1469 1189
y Ff(C)1517 1170 y Fe(2)1578 1120 y Fl(\000)1697 1094
y Fi(e)1678 1120 y Fn(E)1756 1078 y Fk(2)1750 1144 y
Fm(k)1812 1009 y Fi(D)1873 1120 y Fl(r)1975 1094 y Fi(e)1956
1120 y Fn(F)2033 1078 y Fk(2)2019 1144 y Fm(k)2072 1120
y Fn(;)g(\026)2175 1135 y Fm(k)2217 1120 y Fl(r)p Fn(y)2352
1078 y Fk(2)2348 1144 y Fm(k)2391 1009 y Fi(E)2451 1189
y Ff(C)2499 1170 y Fe(2)2555 1005 y Fi(\015)2555 1065
y(\015)2555 1125 y(\015)2616 1172 y Fd(e)2610 1189 y
Fm(L)2658 1170 y Fc(p)3397 1120 y FA(\(5.19\))542 1336
y(+)640 1222 y Fi(\015)640 1281 y(\015)640 1341 y(\015)715
1311 y(e)696 1336 y Fn(G)773 1295 y Fk(1)773 1361 y Fm(k)837
1336 y Fl(\000)956 1311 y Fi(e)937 1336 y Fn(G)1014 1295
y Fk(2)1014 1361 y Fm(k)1057 1222 y Fi(\015)1057 1281
y(\015)1057 1341 y(\015)1118 1388 y Fd(e)1112 1405 y
Fm(L)1160 1386 y Fc(p)3397 1336 y FA(\(5.20\))542 1553
y(+)640 1438 y Fi(\015)640 1498 y(\015)640 1558 y(\015)715
1528 y(e)696 1553 y Fn(E)774 1512 y Fk(1)768 1578 y Fm(k)832
1528 y Fi(e)813 1553 y Fn(F)890 1512 y Fk(1)876 1578
y Fm(k)929 1553 y Fl(r)22 b(\001)g FA(\()p Fn(\026)1181
1568 y Fm(k)1223 1553 y Fl(r)p FA(\010)1376 1568 y Fm(k)1420
1553 y FA(\()p Fn(t)1493 1568 y Fk(1)1532 1553 y FA(\)\))g
Fl(\000)1749 1528 y Fi(e)1730 1553 y Fn(E)1808 1512 y
Fk(2)1802 1578 y Fm(k)1866 1528 y Fi(e)1847 1553 y Fn(F)1924
1512 y Fk(2)1910 1578 y Fm(k)1963 1553 y Fl(r)h(\001)e
FA(\()p Fn(\026)2215 1568 y Fm(k)2258 1553 y Fl(r)p FA(\010)2411
1568 y Fm(k)2454 1553 y FA(\()p Fn(t)2527 1568 y Fk(2)2566
1553 y FA(\)\))2659 1438 y Fi(\015)2659 1498 y(\015)2659
1558 y(\015)2721 1605 y Fd(e)2714 1622 y Fm(L)2762 1603
y Fc(p)3397 1553 y FA(\(5.21\))542 1770 y(+)640 1655
y Fi(\015)640 1715 y(\015)640 1775 y(\015)715 1744 y(e)696
1770 y Fn(E)774 1729 y Fk(1)768 1794 y Fm(k)830 1659
y Fi(D)891 1770 y Fl(r)992 1744 y Fi(e)974 1770 y Fn(F)1051
1729 y Fk(1)1037 1794 y Fm(k)1090 1770 y Fn(;)c(\026)1193
1785 y Fm(k)1235 1770 y Fl(r)p FA(\010)1388 1785 y Fm(k)1431
1770 y FA(\()p Fn(t)1504 1785 y Fk(1)1544 1770 y FA(\))1581
1659 y Fi(E)1642 1839 y Ff(C)1690 1820 y Fe(2)1751 1770
y Fl(\000)1870 1744 y Fi(e)1851 1770 y Fn(E)1929 1729
y Fk(2)1923 1794 y Fm(k)1985 1659 y Fi(D)2046 1770 y
Fl(r)2148 1744 y Fi(e)2129 1770 y Fn(F)2206 1729 y Fk(2)2192
1794 y Fm(k)2245 1770 y Fn(;)g(\026)2348 1785 y Fm(k)2390
1770 y Fl(r)p FA(\010)2543 1785 y Fm(k)2586 1770 y FA(\()p
Fn(t)2659 1785 y Fk(2)2699 1770 y FA(\))2737 1659 y Fi(E)2798
1839 y Ff(C)2846 1820 y Fe(2)2901 1655 y Fi(\015)2901
1715 y(\015)2901 1775 y(\015)2963 1822 y Fd(e)2956 1839
y Fm(L)3004 1820 y Fc(p)3045 1770 y Fn(:)325 b FA(\(5.22\))120
1962 y(W)-8 b(e)30 b(estimate)h(the)g(addends)g(on)f(the)g(righ)m(t)g
(hand)g(side)h(separately)h(and)e(will)g(sho)m(w)h(that)f(eac)m(h)120
2107 y(of)37 b(them)g(has)h(an)f(upp)s(er)h(b)s(ound)f(as)g(claimed)h
(in)g(\(5.17\))o(.)57 b(F)-8 b(or)36 b(the)i(\014rst)g(term)f(on)g(the)
h(righ)m(t)120 2251 y(hand)f(side)h(of)43 b(\(5.18\))36
b(this)h(follo)m(ws)h(directly)g(from)e(Assumption)i(4.1.iv)f(and)g
(Lemma)g(4.11.)120 2396 y(The)d(second)f(addend)h(can)f(b)s(e)f
(estimated)696 2504 y Fi(\015)696 2564 y(\015)752 2589
y Fn(y)804 2547 y Fk(1)800 2613 y Fm(k)864 2589 y Fl(\000)23
b Fn(y)1016 2547 y Fk(2)1012 2613 y Fm(k)1055 2504 y
Fi(\015)1055 2564 y(\015)1116 2611 y Fd(e)1110 2628 y
Fm(L)1158 2609 y Fc(p)1226 2589 y Fl(\024)28 b(k)p Fr(y)1440
2604 y Fk(1)1502 2589 y Fl(\000)22 b Fr(y)1660 2604 y
Fk(2)1700 2589 y Fl(k)1754 2603 y Fd(e)1750 2619 y Fb(L)1799
2600 y Fc(p)1866 2589 y Fl(\024)1972 2504 y Fi(\015)1972
2564 y(\015)2027 2589 y Fl(A)2107 2547 y Fh(\000)p Fm(\013)2107
2613 y Fk(0)2211 2504 y Fi(\015)2211 2564 y(\015)2266
2628 y Fh(B)r Fk(\()2346 2611 y Fd(e)2341 2628 y Fb(L)2390
2609 y Fc(p)2426 2628 y Fk(\))2475 2589 y Fl(k)o Fr(w)2605
2604 y Fk(1)2667 2589 y Fl(\000)h Fr(w)2848 2604 y Fk(2)2887
2589 y Fl(k)2942 2603 y Fd(e)2937 2619 y Fb(L)2986 2600
y Fc(p)3043 2589 y Fn(:)120 2781 y FA(The)34 b(norm)e(\(5.19\))g(can)h
(b)s(e)g(estimated)203 2885 y Fi(\015)203 2944 y(\015)203
3004 y(\015)278 2974 y(e)258 2999 y Fn(E)336 2958 y Fk(1)330
3024 y Fm(k)392 2889 y Fi(D)453 2999 y Fl(r)555 2974
y Fi(e)536 2999 y Fn(F)613 2958 y Fk(1)599 3024 y Fm(k)652
2999 y Fn(;)17 b(\026)755 3014 y Fm(k)798 2999 y Fl(r)p
Fn(y)933 2958 y Fk(1)929 3024 y Fm(k)971 2889 y Fi(E)1032
3068 y Ff(C)1080 3049 y Fe(2)1141 2999 y Fl(\000)1260
2974 y Fi(e)1241 2999 y Fn(E)1319 2958 y Fk(2)1313 3024
y Fm(k)1375 2889 y Fi(D)1435 2999 y Fl(r)1537 2974 y
Fi(e)1518 2999 y Fn(F)1595 2958 y Fk(2)1581 3024 y Fm(k)1635
2999 y Fn(;)g(\026)1738 3014 y Fm(k)1780 2999 y Fl(r)p
Fn(y)1915 2958 y Fk(2)1911 3024 y Fm(k)1953 2889 y Fi(E)2014
3068 y Ff(C)2062 3049 y Fe(2)2117 2885 y Fi(\015)2117
2944 y(\015)2117 3004 y(\015)2179 3051 y Fd(e)2173 3068
y Fm(L)2221 3049 y Fc(p)217 3202 y Fl(\024)322 3118 y
Fi(\015)322 3177 y(\015)377 3202 y FA(\()435 3177 y Fi(e)415
3202 y Fn(E)493 3161 y Fk(1)487 3227 y Fm(k)555 3202
y Fl(\000)674 3177 y Fi(e)655 3202 y Fn(E)733 3161 y
Fk(2)727 3227 y Fm(k)772 3202 y FA(\))810 3122 y Fi(\012)857
3202 y Fl(r)959 3177 y Fi(e)940 3202 y Fn(F)1017 3161
y Fk(1)1003 3227 y Fm(k)1056 3202 y Fn(;)g(\026)1159
3217 y Fm(k)1201 3202 y Fl(r)p Fn(y)1336 3161 y Fk(1)1332
3227 y Fm(k)1375 3122 y Fi(\013)1422 3241 y Ff(C)1470
3222 y Fe(2)1509 3118 y Fi(\015)1509 3177 y(\015)1570
3225 y Fd(e)1564 3241 y Fm(L)1612 3222 y Fc(p)1674 3202
y FA(+)1772 3118 y Fi(\015)1772 3177 y(\015)j(e)1828
3202 y Fn(E)1906 3161 y Fk(2)1900 3227 y Fm(k)1945 3122
y Fi(\012)1992 3202 y Fl(r)p FA(\()2132 3177 y Fi(e)2113
3202 y Fn(F)2190 3161 y Fk(1)2176 3227 y Fm(k)2251 3202
y Fl(\000)2370 3177 y Fi(e)2351 3202 y Fn(F)2428 3161
y Fk(2)2414 3227 y Fm(k)2467 3202 y FA(\))p Fn(;)d(\026)2608
3217 y Fm(k)2650 3202 y Fl(r)p Fn(y)2785 3161 y Fk(1)2781
3227 y Fm(k)2824 3122 y Fi(\013)2871 3241 y Ff(C)2919
3222 y Fe(2)2958 3118 y Fi(\015)2958 3177 y(\015)3019
3225 y Fd(e)3013 3241 y Fm(L)3061 3222 y Fc(p)1193 3372
y FA(+)1291 3287 y Fi(\015)1291 3347 y(\015)j(e)1347
3372 y Fn(E)1425 3331 y Fk(2)1419 3396 y Fm(k)1464 3291
y Fi(\012)1511 3372 y Fl(r)1613 3347 y Fi(e)1594 3372
y Fn(F)1671 3331 y Fk(2)1657 3396 y Fm(k)1710 3372 y
Fn(;)d(\026)1813 3387 y Fm(k)1855 3372 y Fl(r)p FA(\()p
Fn(y)2028 3331 y Fk(1)2024 3396 y Fm(k)2089 3372 y Fl(\000)23
b Fn(y)2241 3331 y Fk(2)2237 3396 y Fm(k)2279 3372 y
FA(\))2317 3291 y Fi(\013)2364 3411 y Ff(C)2412 3392
y Fe(2)2451 3287 y Fi(\015)2451 3347 y(\015)2513 3394
y Fd(e)2506 3411 y Fm(L)2554 3392 y Fc(p)217 3541 y Fl(\024)322
3456 y Fi(\015)322 3516 y(\015)d(e)377 3541 y Fn(E)455
3500 y Fk(1)449 3566 y Fm(k)517 3541 y Fl(\000)636 3516
y Fi(e)617 3541 y Fn(E)695 3500 y Fk(2)689 3566 y Fm(k)734
3456 y Fi(\015)734 3516 y(\015)796 3563 y Fd(e)789 3580
y Fm(L)837 3561 y Fg(1)907 3456 y Fi(\015)907 3516 y(\015)f(e)962
3541 y Fn(F)1039 3500 y Fk(1)1025 3566 y Fm(k)1078 3456
y Fi(\015)1078 3516 y(\015)1149 3563 y Fd(e)1133 3580
y Fm(H)1196 3561 y Fe(1)p Fc(;q)1284 3541 y Fn(\026)1343
3500 y Fh(\017)1383 3541 y Fl(k)p Fr(y)1492 3556 y Fk(1)1531
3541 y Fl(k)1593 3555 y Fd(e)1581 3572 y Fb(H)1644 3553
y Fe(1)p Fc(;q)1754 3541 y FA(+)1852 3456 y Fi(\015)1852
3516 y(\015)h(e)1908 3541 y Fn(E)1986 3500 y Fk(2)1980
3566 y Fm(k)2025 3456 y Fi(\015)2025 3516 y(\015)2087
3563 y Fd(e)2080 3580 y Fm(L)2128 3561 y Fg(1)2198 3456
y Fi(\015)2198 3516 y(\015)f(e)2253 3541 y Fn(F)2330
3500 y Fk(1)2316 3566 y Fm(k)2391 3541 y Fl(\000)2510
3516 y Fi(e)2491 3541 y Fn(F)2568 3500 y Fk(2)2554 3566
y Fm(k)2607 3456 y Fi(\015)2607 3516 y(\015)2678 3563
y Fd(e)2662 3580 y Fm(H)2725 3561 y Fe(1)p Fc(;q)2813
3541 y Fn(\026)2872 3500 y Fh(\017)2911 3541 y Fl(k)p
Fr(y)3020 3556 y Fk(1)3060 3541 y Fl(k)3122 3555 y Fd(e)3110
3572 y Fb(H)3173 3553 y Fe(1)p Fc(;q)2047 3731 y FA(+)2145
3646 y Fi(\015)2145 3706 y(\015)h(e)2200 3731 y Fn(E)2278
3690 y Fk(2)2272 3756 y Fm(k)2318 3646 y Fi(\015)2318
3706 y(\015)2379 3753 y Fd(e)2373 3770 y Fm(L)2421 3751
y Fg(1)2490 3646 y Fi(\015)2490 3706 y(\015)f(e)2545
3731 y Fn(F)2622 3690 y Fk(2)2608 3756 y Fm(k)2662 3646
y Fi(\015)2662 3706 y(\015)2733 3753 y Fd(e)2717 3770
y Fm(H)2780 3751 y Fe(1)p Fc(;q)2868 3731 y Fn(\026)2927
3690 y Fh(\017)2966 3731 y Fl(k)p Fr(y)3075 3746 y Fk(1)3137
3731 y Fl(\000)j Fr(y)3295 3746 y Fk(2)3335 3731 y Fl(k)3397
3745 y Fd(e)3385 3762 y Fb(H)3448 3743 y Fe(1)p Fc(;q)3536
3731 y Fn(:)120 3924 y FA(T)-8 b(aking)30 b(in)m(to)g(accoun)m(t)h
(Lemma)f(5.7)f(and)h(dom)17 b Fl(A)1962 3888 y Fm(\013)1962
3948 y Fk(0)2039 3924 y Fn(,)-17 b Fl(!)28 b Fr(H)2265
3888 y Fk(1)p Fm(;q)2357 3924 y Fn(;)i FA(cf.)43 b(Theorem)31
b(5.4,)f(w)m(e)g(con)m(tin)m(ue)655 4117 y Fl(\024)e
Fn(\026)819 4075 y Fh(\017)858 4117 y Fn(\024)p FA(\(2)p
Fn(R)23 b FA(+)f(1\))1297 4091 y Fi(b)1283 4117 y Fl(E)1336
4144 y Fh(A)1392 4114 y Fg(\000)p Fc(\013)1392 4165 y
Fe(0)1484 4144 y Fm(B)1537 4155 y Fc(R)1616 4091 y Fi(b)1592
4117 y Fl(F)1664 4144 y Fh(A)1720 4114 y Fg(\000)p Fc(\013)1720
4165 y Fe(0)1812 4144 y Fm(B)1865 4155 y Fc(R)1936 4036
y Fi(\000)1982 4117 y Fl(j)p Fn(t)2045 4132 y Fk(1)2106
4117 y Fl(\000)h Fn(t)2241 4132 y Fk(2)2281 4117 y Fl(j)2309
4075 y Fm(\021)2372 4117 y FA(+)f Fl(k)p Fr(w)2601 4132
y Fk(1)2663 4117 y Fl(\000)g Fr(w)2843 4132 y Fk(2)2883
4117 y Fl(k)2938 4131 y Fd(e)2933 4147 y Fb(L)2982 4128
y Fc(p)3022 4036 y Fi(\001)3084 4117 y Fn(:)120 4309
y FA(As)33 b(for)f(the)h(term)g(\(5.20\))f(one)h(obtains)g(according)g
(to)f(Assumption)i(4.1.iii)f(and)g(\(5.9\))203 4412 y
Fi(\015)203 4472 y(\015)203 4532 y(\015)277 4502 y(e)258
4527 y Fn(G)335 4486 y Fk(1)335 4552 y Fm(k)400 4527
y Fl(\000)519 4502 y Fi(e)500 4527 y Fn(G)577 4486 y
Fk(2)577 4552 y Fm(k)619 4412 y Fi(\015)619 4472 y(\015)619
4532 y(\015)681 4579 y Fd(e)675 4596 y Fm(L)723 4577
y Fc(p)791 4527 y Fl(\024)28 b(G)955 4554 y Fh(A)1011
4525 y Fg(\000)p Fc(\013)1011 4576 y Fe(0)1104 4554 y
Fm(B)1157 4565 y Fc(R)1228 4527 y FA(\()p Fl(j)p Fn(t)1329
4542 y Fk(1)1390 4527 y Fl(\000)23 b Fn(t)1525 4542 y
Fk(2)1565 4527 y Fl(j)1593 4486 y Fm(\021)1656 4527 y
FA(+)f Fl(k)p Fr(y)1863 4542 y Fk(1)1925 4527 y Fl(\000)h
Fr(y)2084 4542 y Fk(2)2123 4527 y Fl(k)2173 4544 y Fb(H)2236
4525 y Fe(1)p Fc(;q)2324 4527 y FA(\))1650 4730 y Fl(\024)28
b(G)1814 4758 y Fh(A)1870 4728 y Fg(\000)p Fc(\013)1870
4779 y Fe(0)1963 4758 y Fm(B)2016 4769 y Fc(R)2071 4730
y FA(\(1)21 b(+)h Fn(\024)p FA(\))2388 4650 y Fi(\000)2434
4730 y Fl(j)p Fn(t)2497 4745 y Fk(1)2558 4730 y Fl(\000)h
Fn(t)2693 4745 y Fk(2)2733 4730 y Fl(j)2761 4689 y Fm(\021)2824
4730 y FA(+)f Fl(k)p Fr(w)3053 4745 y Fk(1)3115 4730
y Fl(\000)g Fr(w)3295 4745 y Fk(2)3335 4730 y Fl(k)3390
4744 y Fd(e)3385 4761 y Fb(L)3434 4742 y Fc(p)3474 4650
y Fi(\001)3536 4730 y Fn(:)120 4923 y FA(The)34 b(term)f(\(5.21\))e
(can)i(b)s(e)g(estimated)203 5056 y Fi(\015)203 5116
y(\015)20 b(e)258 5141 y Fn(E)336 5100 y Fk(1)330 5165
y Fm(k)395 5116 y Fi(e)376 5141 y Fn(F)453 5100 y Fk(1)439
5165 y Fm(k)492 5141 y Fl(r)i(\001)g FA(\()p Fn(\026)744
5156 y Fm(k)786 5141 y Fl(r)p FA(\010)939 5156 y Fm(k)982
5141 y FA(\()p Fn(t)1055 5156 y Fk(1)1095 5141 y FA(\)\))g
Fl(\000)1312 5116 y Fi(e)1293 5141 y Fn(E)1371 5100 y
Fk(2)1365 5165 y Fm(k)1429 5116 y Fi(e)1410 5141 y Fn(F)1487
5100 y Fk(2)1473 5165 y Fm(k)1526 5141 y Fl(r)g(\001)g
FA(\()p Fn(\026)1778 5156 y Fm(k)1821 5141 y Fl(r)p FA(\010)1974
5156 y Fm(k)2017 5141 y FA(\()p Fn(t)2090 5156 y Fk(2)2129
5141 y FA(\)\))2222 5056 y Fi(\015)2222 5116 y(\015)2283
5163 y Fd(e)2277 5180 y Fm(L)2325 5161 y Fc(p)989 5310
y Fl(\024)1094 5225 y Fi(\015)1094 5285 y(\015)e(e)1149
5310 y Fn(E)1227 5269 y Fk(1)1221 5335 y Fm(k)1285 5285
y Fi(e)1267 5310 y Fn(F)1344 5269 y Fk(1)1330 5335 y
Fm(k)1405 5310 y Fl(\000)1524 5285 y Fi(e)1504 5310 y
Fn(E)1582 5269 y Fk(2)1576 5335 y Fm(k)1641 5285 y Fi(e)1622
5310 y Fn(F)1699 5269 y Fk(2)1685 5335 y Fm(k)1738 5225
y Fi(\015)1738 5285 y(\015)1800 5332 y Fd(e)1793 5349
y Fm(L)1841 5330 y Fg(1)1911 5225 y Fi(\015)1911 5285
y(\015)1966 5310 y Fl(r)i(\001)g FA(\()p Fn(\026)2218
5325 y Fm(k)2260 5310 y Fl(r)p FA(\010)2413 5325 y Fm(k)2456
5310 y FA(\()p Fn(t)2529 5325 y Fk(1)2569 5310 y FA(\)\))2661
5225 y Fi(\015)2661 5285 y(\015)2723 5332 y Fd(e)2717
5349 y Fm(L)2765 5330 y Fc(p)1281 5479 y FA(+)1379 5395
y Fi(\015)1379 5455 y(\015)1454 5454 y(e)1435 5479 y
Fn(E)1513 5438 y Fk(2)1507 5504 y Fm(k)1571 5454 y Fi(e)1552
5479 y Fn(F)1629 5438 y Fk(2)1615 5504 y Fm(k)1668 5395
y Fi(\015)1668 5455 y(\015)1730 5502 y Fd(e)1724 5519
y Fm(L)1772 5500 y Fg(1)1841 5395 y Fi(\015)1841 5455
y(\015)1896 5479 y Fl(r)g(\001)g FA(\()p Fn(\026)2148
5494 y Fm(k)2190 5479 y Fl(r)p FA(\010)2343 5494 y Fm(k)2386
5479 y FA(\()p Fn(t)2459 5494 y Fk(1)2499 5479 y FA(\)\))g
Fl(\000)h(r)f(\001)g FA(\()p Fn(\026)2949 5494 y Fm(k)2991
5479 y Fl(r)p FA(\010)3144 5494 y Fm(k)3187 5479 y FA(\()p
Fn(t)3260 5494 y Fk(2)3300 5479 y FA(\)\))3392 5395 y
Fi(\015)3392 5455 y(\015)3454 5502 y Fd(e)3448 5519 y
Fm(L)3496 5500 y Fc(p)3536 5479 y Fn(:)p 120 5702 3526
4 v 290 5823 a Fx(Preprin)n(t)k(765,)h(W)-7 b(eierstra\031{Institut)26
b(f)1556 5827 y(\177)1554 5823 y(ur)i(Angew)n(andte)f(Analysis)g(und)h
(Sto)r(c)n(hastik,)f(Berlin)g(2002)p eop
%%Page: 20 22
20 21 bop 120 144 a Fr(20)118 b Fs(Hans-Christoph)37
b(Kaiser,)g(Ha)n(gen)g(Neidhardt,)h(and)g(Jo)n(a)n(chim)h(Rehber)n(g)p
120 183 3526 4 v 120 383 a FA(According)28 b(to)f(\(5.10\),)h(\(5.16\))
f(Lemma)h(5.7,)g(and)f(Assumption)j(4.1.iv)d(this)h(term)g(is)g(b)s
(ounded)120 527 y(from)k(ab)s(o)m(v)m(e)i(b)m(y)339 762
y(3)17 b Fn(\025)492 737 y Fi(b)479 762 y Fl(E)532 790
y Fh(A)588 760 y Fg(\000)p Fc(\013)588 811 y Fe(0)679
790 y Fm(B)732 801 y Fc(R)811 737 y Fi(b)786 762 y Fl(F)858
790 y Fh(A)914 760 y Fg(\000)p Fc(\013)914 811 y Fe(0)1007
790 y Fm(B)1060 801 y Fc(R)1114 678 y Fi(\015)1114 737
y(\015)1170 762 y Fl(r)22 b(\001)g FA(\()p Fn(\026)1422
777 y Fm(k)1464 762 y Fl(r)p FA(\010)1617 777 y Fm(k)1660
762 y FA(\))1715 678 y Fi(\015)1715 737 y(\015)1770 801
y Fm(C)1825 782 y Fc(\021)1863 801 y Fk(\([)p Fm(T)1951
810 y Fe(0)1986 801 y Fm(;T)2047 810 y Fe(1)2081 801
y Fk(];)2127 785 y Fd(e)2121 801 y Fm(L)2169 782 y Fc(p)2204
801 y Fk(\))2252 682 y Fi(\000)2298 762 y Fl(j)p Fn(t)2361
777 y Fk(1)2423 762 y Fl(\000)g Fn(t)2557 777 y Fk(2)2597
762 y Fl(j)2625 721 y Fm(\021)2689 762 y FA(+)g Fl(k)p
Fr(w)2918 777 y Fk(1)2979 762 y Fl(\000)h Fr(w)3160 777
y Fk(2)3199 762 y Fl(k)3254 776 y Fd(e)3249 793 y Fb(L)3298
774 y Fc(p)3338 682 y Fi(\001)3400 762 y Fn(:)120 997
y FA(Finally)-8 b(,)33 b(the)g(term)g(\(5.22\))f(can)h(b)s(e)f(treated)
h(as)g(follo)m(ws:)203 1142 y Fi(\015)203 1202 y(\015)203
1262 y(\015)278 1232 y(e)258 1257 y Fn(E)336 1216 y Fk(1)330
1282 y Fm(k)392 1146 y Fi(D)453 1257 y Fl(r)555 1232
y Fi(e)536 1257 y Fn(F)613 1216 y Fk(1)599 1282 y Fm(k)652
1257 y Fn(;)17 b(\026)755 1272 y Fm(k)798 1257 y Fl(r)p
FA(\010)951 1272 y Fm(k)994 1257 y FA(\()p Fn(t)1067
1272 y Fk(1)1106 1257 y FA(\))1144 1146 y Fi(E)1205 1326
y Ff(C)1253 1307 y Fe(2)1314 1257 y Fl(\000)1433 1232
y Fi(e)1414 1257 y Fn(E)1492 1216 y Fk(2)1486 1282 y
Fm(k)1548 1146 y Fi(D)1609 1257 y Fl(r)1710 1232 y Fi(e)1692
1257 y Fn(F)1769 1216 y Fk(2)1755 1282 y Fm(k)1808 1257
y Fn(;)g(\026)1911 1272 y Fm(k)1953 1257 y Fl(r)p FA(\010)2106
1272 y Fm(k)2149 1257 y FA(\()p Fn(t)2222 1272 y Fk(2)2262
1257 y FA(\))2299 1146 y Fi(E)2360 1326 y Ff(C)2408 1307
y Fe(2)2464 1142 y Fi(\015)2464 1202 y(\015)2464 1262
y(\015)2525 1309 y Fd(e)2519 1326 y Fm(L)2567 1307 y
Fc(p)217 1474 y Fl(\024)322 1359 y Fi(\015)322 1419 y(\015)322
1479 y(\015)394 1363 y(\020)473 1449 y(e)453 1474 y Fn(E)531
1433 y Fk(1)525 1498 y Fm(k)593 1474 y Fl(\000)712 1449
y Fi(e)693 1474 y Fn(E)771 1433 y Fk(2)765 1498 y Fm(k)810
1363 y Fi(\021)g(D)947 1474 y Fl(r)1049 1449 y Fi(e)1030
1474 y Fn(F)1107 1433 y Fk(1)1093 1498 y Fm(k)1146 1474
y Fn(;)g(\026)1249 1489 y Fm(k)1291 1474 y Fl(r)p FA(\010)1444
1489 y Fm(k)1488 1474 y FA(\()p Fn(t)1561 1489 y Fk(1)1600
1474 y FA(\))1638 1363 y Fi(E)1699 1543 y Ff(C)1747 1524
y Fe(2)1802 1359 y Fi(\015)1802 1419 y(\015)1802 1479
y(\015)1864 1526 y Fd(e)1858 1543 y Fm(L)1906 1524 y
Fc(p)1064 1690 y FA(+)1162 1576 y Fi(\015)1162 1636 y(\015)1162
1695 y(\015)1236 1665 y(e)1217 1690 y Fn(E)1295 1649
y Fk(2)1289 1715 y Fm(k)1351 1580 y Fi(D)1412 1690 y
Fl(r)p FA(\()1552 1665 y Fi(e)1533 1690 y Fn(F)1610 1649
y Fk(1)1596 1715 y Fm(k)1671 1690 y Fl(\000)1790 1665
y Fi(e)1771 1690 y Fn(F)1848 1649 y Fk(2)1834 1715 y
Fm(k)1887 1690 y FA(\))p Fn(;)g(\026)2028 1705 y Fm(k)2070
1690 y Fl(r)p FA(\010)2223 1705 y Fm(k)2266 1690 y FA(\()p
Fn(t)2339 1705 y Fk(1)2379 1690 y FA(\))2417 1580 y Fi(E)2477
1759 y Ff(C)2525 1740 y Fe(2)2581 1576 y Fi(\015)2581
1636 y(\015)2581 1695 y(\015)2643 1743 y Fd(e)2636 1759
y Fm(L)2684 1740 y Fc(p)1765 1907 y FA(+)1863 1793 y
Fi(\015)1863 1852 y(\015)1863 1912 y(\015)1938 1882 y(e)1919
1907 y Fn(E)1997 1866 y Fk(2)1991 1932 y Fm(k)2053 1797
y Fi(D)2114 1907 y Fl(r)2216 1882 y Fi(e)2197 1907 y
Fn(F)2274 1866 y Fk(1)2260 1932 y Fm(k)2313 1907 y Fn(;)g(\026)2416
1922 y Fm(k)2458 1907 y Fl(r)p FA(\(\010)2649 1922 y
Fm(k)2692 1907 y FA(\()p Fn(t)2765 1922 y Fk(1)2805 1907
y FA(\))22 b Fl(\000)g FA(\010)3034 1922 y Fm(k)3077
1907 y FA(\()p Fn(t)3150 1922 y Fk(2)3190 1907 y FA(\))3228
1797 y Fi(E)3289 1976 y Ff(C)3337 1957 y Fe(2)3392 1793
y Fi(\015)3392 1852 y(\015)3392 1912 y(\015)3454 1959
y Fd(e)3448 1976 y Fm(L)3496 1957 y Fc(p)3536 1907 y
Fn(:)120 2142 y FA(Making)33 b(use)h(of)39 b(\(2.1\))32
b(w)m(e)h(con)m(tin)m(ue)231 2402 y Fl(\024)336 2317
y Fi(\015)336 2377 y(\015)20 b(e)391 2402 y Fn(E)469
2361 y Fk(1)463 2426 y Fm(k)531 2402 y Fl(\000)650 2377
y Fi(e)630 2402 y Fn(E)708 2361 y Fk(2)702 2426 y Fm(k)748
2317 y Fi(\015)748 2377 y(\015)810 2424 y Fd(e)803 2441
y Fm(L)851 2422 y Fg(1)920 2317 y Fi(\015)920 2377 y(\015)g(e)976
2402 y Fn(F)1053 2361 y Fk(1)1039 2426 y Fm(k)1092 2317
y Fi(\015)1092 2377 y(\015)1163 2424 y Fd(e)1147 2441
y Fm(H)1210 2422 y Fe(1)p Fc(;q)1298 2402 y Fn(\026)1357
2361 y Fh(\017)1396 2317 y Fi(\015)1396 2377 y(\015)1452
2402 y FA(\010)1522 2417 y Fm(k)1565 2402 y FA(\()p Fn(t)1638
2417 y Fk(1)1677 2402 y FA(\))1715 2317 y Fi(\015)1715
2377 y(\015)1787 2424 y Fd(e)1771 2441 y Fm(H)1834 2422
y Fe(1)p Fc(;q)1053 2592 y FA(+)1151 2507 y Fi(\015)1151
2567 y(\015)g(e)1206 2592 y Fn(E)1284 2551 y Fk(2)1278
2616 y Fm(k)1324 2507 y Fi(\015)1324 2567 y(\015)1385
2614 y Fd(e)1379 2631 y Fm(L)1427 2612 y Fg(1)1496 2507
y Fi(\015)1496 2567 y(\015)f(e)1552 2592 y Fn(F)1629
2551 y Fk(1)1615 2616 y Fm(k)1690 2592 y Fl(\000)1808
2567 y Fi(e)1789 2592 y Fn(F)1866 2551 y Fk(2)1852 2616
y Fm(k)1906 2507 y Fi(\015)1906 2567 y(\015)1977 2614
y Fd(e)1961 2631 y Fm(H)2024 2612 y Fe(1)p Fc(;q)2112
2592 y Fn(\026)2171 2551 y Fh(\017)2210 2507 y Fi(\015)2210
2567 y(\015)2265 2592 y FA(\010)2335 2607 y Fm(k)2378
2592 y FA(\()p Fn(t)2451 2607 y Fk(1)2491 2592 y FA(\))2529
2507 y Fi(\015)2529 2567 y(\015)2600 2614 y Fd(e)2584
2631 y Fm(H)2647 2612 y Fe(1)p Fc(;q)1733 2782 y FA(+)1831
2697 y Fi(\015)1831 2757 y(\015)1906 2756 y(e)1886 2782
y Fn(E)1964 2741 y Fk(2)1958 2806 y Fm(k)2004 2697 y
Fi(\015)2004 2757 y(\015)2065 2804 y Fd(e)2059 2821 y
Fm(L)2107 2802 y Fg(1)2176 2697 y Fi(\015)2176 2757 y(\015)2250
2756 y(e)2232 2782 y Fn(F)2309 2741 y Fk(1)2295 2806
y Fm(k)2348 2697 y Fi(\015)2348 2757 y(\015)2419 2804
y Fd(e)2403 2821 y Fm(H)2466 2802 y Fe(1)p Fc(;q)2554
2782 y Fn(\026)2613 2741 y Fh(\017)2652 2697 y Fi(\015)2652
2757 y(\015)2708 2782 y FA(\010)2778 2797 y Fm(k)2821
2782 y FA(\()p Fn(t)2894 2797 y Fk(1)2933 2782 y FA(\))j
Fl(\000)h FA(\010)3163 2797 y Fm(k)3206 2782 y FA(\()p
Fn(t)3279 2797 y Fk(2)3319 2782 y FA(\))3357 2697 y Fi(\015)3357
2757 y(\015)3428 2804 y Fd(e)3412 2821 y Fm(H)3475 2802
y Fe(1)p Fc(;q)120 3017 y FA(and)33 b(b)m(y)g(means)h(of)e(Lemma)h(5.7)
f(and)h(Assumption)h(4.1.iv)f(w)m(e)h(\014nish)f(this)h(estimate)524
3251 y Fl(\024)643 3226 y Fi(b)629 3251 y Fl(E)682 3279
y Fh(A)738 3249 y Fg(\000)p Fc(\013)738 3300 y Fe(0)830
3279 y Fm(B)883 3290 y Fc(R)962 3226 y Fi(b)938 3251
y Fl(F)1010 3279 y Fh(A)1066 3249 y Fg(\000)p Fc(\013)1066
3300 y Fe(0)1158 3279 y Fm(B)1211 3290 y Fc(R)1265 3251
y Fn(\026)1324 3210 y Fh(\017)1364 3167 y Fi(\015)1364
3227 y(\015)1419 3251 y Fr(\010)1500 3167 y Fi(\015)1500
3227 y(\015)1555 3290 y Fm(C)1610 3272 y Fc(\021)1648
3290 y Fk(\([)p Fm(T)1736 3299 y Fe(0)1771 3290 y Fm(;T)1832
3299 y Fe(1)1866 3290 y Fk(];)1918 3273 y Fd(e)1906 3290
y Fb(H)1969 3272 y Fe(1)p Fc(;q)2053 3290 y Fk(\))2084
3171 y Fi(\000)2130 3251 y Fl(j)p Fn(t)2193 3266 y Fk(1)2254
3251 y Fl(\000)23 b Fn(t)2389 3266 y Fk(2)2429 3251 y
Fl(j)2457 3210 y Fm(\021)2520 3251 y FA(+)f Fl(k)p Fr(w)2749
3266 y Fk(1)2811 3251 y Fl(\000)g Fr(w)2991 3266 y Fk(2)3031
3251 y Fl(k)3086 3265 y Fd(e)3081 3282 y Fb(L)3130 3263
y Fc(p)3170 3171 y Fi(\001)3215 3251 y Fn(:)p 3575 3486
4 66 v 3579 3424 59 4 v 3579 3486 V 3637 3486 4 66 v
120 3706 a Fr(5.10)38 b(Theorem.)k Fo(Pr)-5 b(oblem)34
b(4.12)g(admits)h(exactly)f(one)h(solution)697 3941 y
Fr(v)29 b Fl(2)f Fn(C)7 b FA(\([)p Fn(T)1078 3956 y Fk(0)1118
3941 y Fn(;)17 b(T)d FA(])p Fn(;)j FA(dom)f Fl(A)1584
3900 y Fm(\013)1584 3965 y Fk(0)1633 3941 y FA(\))22
b Fl(\\)h Fn(C)7 b FA(\(])p Fn(T)1981 3956 y Fk(0)2020
3941 y Fn(;)17 b(T)d FA(])p Fn(;)j Fl(D)s FA(\))k Fl(\\)i
Fn(C)2511 3900 y Fk(1)2550 3941 y FA(\(])p Fn(T)2672
3956 y Fk(0)2712 3941 y Fn(;)17 b(T)d FA(])p Fn(;)2903
3915 y Fi(e)2898 3941 y Fr(L)2965 3900 y Fm(p)3004 3941
y FA(\))p Fn(:)120 4176 y Fo(The)34 b(function)h Fr(u)28
b FA(:=)f Fr(v)d FA(+)e Fr(\010)35 b Fo(is)g(a)f(lo)-5
b(c)g(al)35 b(solution)f(of)56 b FA(\(1.1\))34 b Fo(in)h(the)g(sense)f
(of)g(De\014nition)g(4.7.)120 4439 y(Pr)-5 b(o)g(of.)48
b FA(The)36 b(\014rst)f(assertion)g(is)g(implied)h(b)m(y)f(Prop)s
(osition)g(3.7)f(whic)m(h)i(applies)g(with)f(resp)s(ect)120
4584 y(to)d(the)h(Banac)m(h)g(space)h Fn(X)h FA(:=)1269
4558 y Fi(e)1263 4584 y Fr(L)1330 4548 y Fm(p)1402 4584
y FA(to)d(the)h(op)s(erators)f Fl(A)2200 4599 y Fk(0)2272
4584 y FA(and)g Fl(A)p FA(\()p Fn(t;)17 b Fr(w)r FA(\))31
b(from)h(De\014nition)h(5.5.)120 4728 y(According)46
b(to)f(Theorem)h(5.3,)i(Theorem)e(5.8,)i(and)d(Theorem)i(5.9)d(the)i
(preconditions)g(of)120 4873 y(Prop)s(osition)25 b(3.7)g(on)f(the)i(op)
s(erators)e(and)h(the)h(righ)m(t)f(hand)g(side)h(of)e(the)h(equation)h
(are)f(ful\014lled.)120 5017 y(As)30 b(for)f(the)h(initial)f(v)-5
b(alue,)31 b(\(3.4\))d(from)i(Prop)s(osition)f(3.5)g(implies)i
Fr(u)2649 5032 y Fk(0)2704 5017 y Fl(\000)16 b Fr(\010)p
FA(\()p Fn(T)2973 5032 y Fk(0)3013 5017 y FA(\))27 b
Fl(2)i FA(dom)16 b Fl(A)3453 4970 y Fm(\014)3453 5042
y Fk(0)3529 5017 y FA(for)120 5162 y(an)m(y)33 b Fn(\014)h
Fl(2)p FA(])p Fn(\013)q(;)17 b(\015)5 b FA([)p Fn(:)120
5353 y FA(The)36 b(complex)g(conjugate)p 1151 5297 61
4 v 35 w Fr(v)g FA(of)e Fr(v)j FA(also)e(is)g(a)f(solution)i(of)41
b(\(4.12\))34 b(and)h(has)g(the)g(same)h(initial)120
5498 y(v)-5 b(alue.)44 b(Hence,)34 b Fr(v)29 b FA(=)p
919 5442 V 28 w Fr(v)r FA(,)j(i.e.)44 b Fr(v)34 b FA(tak)m(es)g(its)f
(v)-5 b(alues)34 b(in)f Fj(R)2163 5462 y Fm(l)2221 5498
y FA(and)g(satis\014es)h(\(4.9\).)p 3575 5498 4 66 v
3579 5435 59 4 v 3579 5498 V 3637 5498 4 66 v 120 5702
3526 4 v 290 5823 a Fx(Preprin)n(t)26 b(765,)h(W)-7 b
(eierstra\031{Institut)26 b(f)1556 5827 y(\177)1554 5823
y(ur)i(Angew)n(andte)f(Analysis)g(und)h(Sto)r(c)n(hastik,)f(Berlin)g
(2002)p eop
%%Page: 21 23
21 22 bop 120 144 a Fs(Classical)38 b(Solutions)g(of)g(Quasilinear)g(P)
-9 b(arabolic)38 b(Systems)618 b Fr(21)p 120 183 3526
4 v 120 400 a Fy(Ac)l(kno)l(wledgemen)l(t)120 692 y FA(W)-8
b(e)36 b(w)m(ould)g(lik)m(e)g(to)f(thank)h(Professor)g(Herb)s(ert)g(Ga)
5 b(jewski)36 b(and)g(Professor)g(Konrad)f(Gr)3468 696
y(\177)3468 692 y(oger)120 836 y(for)d(their)h(helpful)h(commen)m(ts)g
(on)e(this)i(pap)s(er.)120 1263 y Fy(References)169 1554
y FA([1])49 b(H.)61 b(Amann,)69 b Fo(Nonhomo)-5 b(gene)g(ous)60
b(line)-5 b(ar)60 b(and)h(quasiline)-5 b(ar)60 b(el)5
b(liptic)60 b(and)h(p)-5 b(ar)g(ab)g(olic)321 1698 y(b)g(oundary)32
b(value)h(pr)-5 b(oblems)p FA(,)30 b(F)-8 b(unction)31
b(spaces,)i(di\013eren)m(tial)f(op)s(erators)e(and)h(nonlinear)321
1843 y(analysis.)42 b(Surv)m(ey)h(articles)e(and)g(comm)m(unications)i
(of)e(the)g(in)m(ternational)g(conference)321 1987 y(held)j(in)g(F)-8
b(riedric)m(hsro)s(da,)47 b(German)m(y)-8 b(,)47 b(Septem)m(b)s(er)f
(20{26,)f(1992.)e(\(Stuttgart\))g(\(H.-J.)321 2132 y(Sc)m(hmeisser)37
b(and)d(H.)h(T)-8 b(rieb)s(el,)36 b(eds.\),)g(T)-8 b(eubner-T)g(exte)36
b(Math.,)g(v)m(ol.)f(133,)f(B.)g(G.)g(T)-8 b(eub-)321
2276 y(ner)33 b(V)-8 b(erlagsgesellsc)m(haft,)35 b(1993,)c(pp.)i
(9{126.)169 2513 y([2])49 b(P)-8 b(.)28 b(G.)f(Ciarlet,)i
Fo(The)h(\014nite)g(element)g(metho)-5 b(d)29 b(for)i(el)5
b(liptic)30 b(pr)-5 b(oblems)p FA(,)27 b(Studies)i(in)f(Math-)321
2657 y(ematics)35 b(and)e(its)i(Applications,)g(North)f(Holland,)g
(Amsterdam,)i(New)e(Y)-8 b(ork,)35 b(Oxford,)321 2802
y(1979.)169 3039 y([3])49 b(M.)25 b(Costab)s(el,)i(M.)f(Dauge,)g(and)f
(S.)h(Nicaise,)i Fo(Singularities)f(of)h(Maxwel)5 b(l)27
b(interfac)-5 b(e)28 b(pr)-5 b(ob-)321 3183 y(lems)p
FA(,)31 b(M2AN,)i(Math.)g(Mo)s(del.)g(Numer.)h(Anal.)f
Fr(33)f FA(\(1999\),)g(no.)h(3,)f(627{649.)169 3420 y([4])49
b(H.)25 b(Ga)5 b(jewski,)29 b Fo(A)n(nalysis)e(und)i(Numerik)f(von)g
(Ladungstr)-5 b(ansp)g(ort)28 b(in)g(Halbleitern)p FA(,)e(Mitt.)321
3564 y(Ges.)33 b(Angew.)g(Math.)g(Mec)m(h.)h Fr(16)f
FA(\(1993\),)e(35.)169 3801 y([5])49 b(H.)39 b(Ga)5 b(jewski,)43
b(K.)c(Gr)1177 3805 y(\177)1177 3801 y(oger,)i(and)f(K.)f(Zac)m
(harias,)j Fo(Nichtline)-5 b(ar)g(e)41 b(Op)-5 b(er)g(ator)g
(gleichungen)321 3946 y(und)34 b(Op)-5 b(er)g(ator)g(di\013er)g
(entialgleichungen)p FA(,)30 b(Ak)-5 b(ademie{V)d(erlag,)34
b(Berlin,)f(1974.)169 4182 y([6])49 b(J.)39 b(A.)h(Griep)s(en)m(trog,)i
(K.)e(Gr)1414 4186 y(\177)1414 4182 y(oger,)h(H.-Chr.)f(Kaiser,)i(and)e
(J.)g(Reh)m(b)s(erg,)i Fo(Interp)-5 b(olation)321 4327
y(for)38 b(function)h(sp)-5 b(ac)g(es)38 b(r)-5 b(elate)g(d)38
b(to)h(mixe)-5 b(d)38 b(b)-5 b(oundary)39 b(value)g(pr)-5
b(oblems)p FA(,)37 b(Mathematisc)m(he)321 4471 y(Nac)m(hric)m(h)m(ten)d
Fr(241)f FA(\(2002\),)f(110{120,)63 b(\(Preprin)m(t)34
b(580,)e(WIAS,)h(Berlin,)h(2000\).)169 4708 y([7])49
b(J.)35 b(A.)h(Griep)s(en)m(trog,)g(H.-Chr.)g(Kaiser,)h(and)e(J.)h(Reh)
m(b)s(erg,)h Fo(He)-5 b(at)38 b(kernel)f(and)g(r)-5 b(esolvent)321
4853 y(pr)g(op)g(erties)32 b(for)i(se)-5 b(c)g(ond)32
b(or)-5 b(der)34 b(el)5 b(liptic)32 b(di\013er)-5 b(ential)33
b(op)-5 b(er)g(ators)33 b(with)g(gener)-5 b(al)33 b(b)-5
b(oundary)321 4997 y(c)g(onditions)47 b(on)i Fn(L)1020
4961 y Fm(p)1060 4997 y FA(,)i(Adv)-5 b(ances)49 b(in)f(Mathematical)h
(Sciences)h(and)e(Applications)h Fr(11)321 5142 y FA(\(2001\),)31
b(no.)i(1,)f(87{112,)64 b(\(Preprin)m(t)34 b(511,)e(WIAS,)h(Berlin,)g
(1999\).)169 5378 y([8])49 b(K.)25 b(Gr)564 5382 y(\177)564
5378 y(oger,)i Fo(A)i Fn(W)1004 5342 y Fk(1)p Fm(;p)1099
5378 y Fo({estimate)f(for)h(solutions)f(to)h(mixe)-5
b(d)28 b(b)-5 b(oundary)29 b(value)f(pr)-5 b(oblems)28
b(for)321 5523 y(se)-5 b(c)g(ond)33 b(or)-5 b(der)35
b(el)5 b(liptic)34 b(di\013er)-5 b(ential)34 b(e)-5 b(quations)p
FA(,)32 b(Math.)h(Ann.)g Fr(283)g FA(\(1989\),)f(679{687.)p
120 5702 V 290 5823 a Fx(Preprin)n(t)26 b(765,)h(W)-7
b(eierstra\031{Institut)26 b(f)1556 5827 y(\177)1554
5823 y(ur)i(Angew)n(andte)f(Analysis)g(und)h(Sto)r(c)n(hastik,)f
(Berlin)g(2002)p eop
%%Page: 22 24
22 23 bop 120 144 a Fr(22)118 b Fs(Hans-Christoph)37
b(Kaiser,)g(Ha)n(gen)g(Neidhardt,)h(and)g(Jo)n(a)n(chim)h(Rehber)n(g)p
120 183 3526 4 v 169 383 a FA([9])49 b(K.)30 b(Gr)569
387 y(\177)569 383 y(oger,)g Fo(W)902 347 y Fk(1)p Fm(;p)997
383 y Fo({estimates)i(of)h(solutions)f(to)i(evolution)e(e)-5
b(quations)32 b(c)-5 b(orr)g(esp)g(onding)32 b(to)321
527 y(nonsmo)-5 b(oth)32 b(se)-5 b(c)g(ond)33 b(or)-5
b(der)34 b(el)5 b(liptic)33 b(di\013er)-5 b(ential)33
b(op)-5 b(er)g(ators)p FA(,)31 b(Nonlinear)h(Anal.)g(Theory)321
672 y(Metho)s(ds)h(Appl.)g Fr(18)g FA(\(1992\),)e(569{577.)120
899 y([10])49 b(K.)25 b(Gr)564 903 y(\177)564 899 y(oger)h(and)g(H.)g
(Ga)5 b(jewski,)28 b Fo(R)-5 b(e)g(action{di\013usion)28
b(pr)-5 b(o)g(c)g(esses)27 b(of)i(ele)-5 b(ctric)g(al)5
b(ly)28 b(char)-5 b(ge)g(d)321 1044 y(sp)g(e)g(cies)p
FA(,)31 b(Math.)i(Nac)m(hr.)g Fr(177)g FA(\(1996\),)e(109{130.)120
1271 y([11])49 b(K.)25 b(Gr)564 1275 y(\177)564 1271
y(oger)g(and)h(J.)g(Reh)m(b)s(erg,)i Fo(R)-5 b(esolvent)28
b(estimates)g(in)g Fn(W)2534 1235 y Fk(1)p Fm(;p)2657
1271 y Fo(for)h(se)-5 b(c)g(ond)27 b(or)-5 b(der)29 b(el)5
b(liptic)321 1416 y(di\013er)-5 b(ential)41 b(op)-5 b(er)g(ators)42
b(in)g(c)-5 b(ase)41 b(of)h(mixe)-5 b(d)42 b(b)-5 b(oundary)42
b(c)-5 b(onditions)p FA(,)42 b(Math.)f(Ann.)g Fr(285)321
1560 y FA(\(1989\),)31 b(105{113.)120 1788 y([12])49
b(H.-Chr.)e(Kaiser,)k(H.)d(Neidhardt,)k(and)47 b(J.)g(Reh)m(b)s(erg,)52
b Fo(V)-7 b(an)48 b(Ro)-5 b(osbr)g(o)g(e)g(ck's)46 b(e)-5
b(quations)321 1932 y(admit)34 b(classic)-5 b(al)34 b(solutions)g(in)h
Fn(L)1570 1896 y Fm(p)1610 1932 y Fo(:)44 b(the)35 b(2d)g(c)-5
b(ase)p FA(,)32 b(in)h(preparation.)120 2160 y([13])49
b(N.)28 b(Mey)m(ers,)k Fo(A)n(n)f Fn(L)1029 2124 y Fm(p)1070
2160 y Fo(-estimate)f(for)i(the)f(gr)-5 b(adient)31 b(of)g(solutions)g
(of)g(se)-5 b(c)g(ond)30 b(or)-5 b(der)32 b(el)5 b(liptic)321
2304 y(diver)-5 b(genc)g(e)31 b(e)-5 b(quations)p FA(,)30
b(Ann.)h(Scuola)g(Norm.)g(Sup.)g(Pisa,)h(Sci.)f(Fis.)f(Mat.,)h(I)s(I)s
(I.)g(Ser.)g Fr(17)321 2449 y FA(\(1963\),)g(189{206.)120
2676 y([14])49 b(S.)j(Selb)s(erherr,)59 b Fo(A)n(nalysis)52
b(and)h(simulation)f(of)h(semic)-5 b(onductor)52 b(devic)-5
b(es)p FA(,)56 b(Springer,)321 2821 y(Wien,)33 b(1984.)120
3048 y([15])49 b(P)-8 b(.)35 b(E.)h(Sob)s(olevskii,)i
Fo(Equations)g(of)f(p)-5 b(ar)g(ab)g(olic)36 b(typ)-5
b(e)38 b(in)f(a)h(Banach)e(sp)-5 b(ac)g(e)p FA(,)35 b(Amer.)i(Mat.)321
3192 y(So)s(c.)32 b(T)-8 b(ransl.)33 b(Ser.)g(2)f Fr(49)g
FA(\(1966\),)f(1{62)h(\(English.)h(Russian)g(original:)44
b(T)-8 b(rudy)33 b(Mosk)m(o)m(v.)321 3337 y(Mat.)f(Obsc.)i
Fr(10)e FA(\(1961\),)g(297{350\).)120 3564 y([16])49
b(R.)41 b(T)-8 b(emam,)46 b Fo(Navier{Stokes)d(e)-5 b(quations)43
b({)g(the)-5 b(ory)44 b(and)f(numeric)-5 b(al)43 b(analysis)p
FA(,)h(North)321 3709 y(Holland)32 b(Publishing)j(Compan)m(y)-8
b(,)33 b(Amsterdam,)h(New)g(Y)-8 b(ork,)33 b(Oxford,)f(1979.)120
3936 y([17])49 b(H.)g(T)-8 b(rieb)s(el,)54 b Fo(Interp)-5
b(olation)49 b(the)-5 b(ory,)54 b(function)c(sp)-5 b(ac)g(es,)53
b(di\013er)-5 b(ential)49 b(op)-5 b(er)g(ators)p FA(,)52
b(Dt.)321 4081 y(V)-8 b(erl.)39 b(d.)g(Wiss.,)j(Berlin,)f(1978,)f
(North)f(Holland,)h(Amsterdam,)i(1978;)f(Mir,)g(Mosco)m(w)321
4225 y(1980.)120 4453 y([18])49 b(J.)85 b(Wlok)-5 b(a,)99
b Fo(Partiel)5 b(le)83 b(Di\013er)-5 b(entialgleichungen)p
FA(,)96 b(T)-8 b(eubner)87 b(V)-8 b(erlagsgesellsc)m(haft)321
4597 y(Leipzig,)33 b(1982.)p 120 5702 V 290 5823 a Fx(Preprin)n(t)26
b(765,)h(W)-7 b(eierstra\031{Institut)26 b(f)1556 5827
y(\177)1554 5823 y(ur)i(Angew)n(andte)f(Analysis)g(und)h(Sto)r(c)n
(hastik,)f(Berlin)g(2002)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF