Literature on Nonlocal Equations

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Contents

2011

Barles, Guy; Chasseigne, Emmanuel; Imbert, Cyril (2011), "Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations", Journal of the European Mathematical Society (JEMS) 13 (1): 1–26, doi:10.4171/JEMS/242, ISSN 1435-9855, http://dx.doi.org/10.4171/JEMS/242 

Bertozzi, Andrea; Laurent, Thomas; Rosado, Jesus (2011), "Lp theory for the multidimensional aggregation equation", Communications on Pure and Applied Mathematics 64 (1): 45–83, doi:10.1002/cpa.20334, ISSN 0010-3640 

Silvestre, Luis (2011), "On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusion", Advances in Mathematics 226 (2): 2020–2039, doi:10.1016/j.aim.2010.09.007, ISSN 0001-8708, http://dx.doi.org/10.1016/j.aim.2010.09.007 

2010

Biler, Piotr; Monneau, Régis; Karch, Grzegorz (2009), "Nonlinear Diffusion of Dislocation Density and Self-Similar Solutions", Communications in Mathematical Physics 294 (1): 145–168, doi:10.1007/s00220-009-0855-8, ISSN 0010-3616 

2009

Barlow, Martin T.; Bass, Richard F.; Chen, Zhen-Qing; Kassmann, Moritz (2009), "Non-local Dirichlet forms and symmetric jump processes", Transactions of the American Mathematical Society 361 (4): 1963–1999, doi:10.1090/S0002-9947-08-04544-3, ISSN 0002-9947, http://dx.doi.org/10.1090/S0002-9947-08-04544-3 

Constantin, Peter; Wu, Jiahong (2009), "Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations", Annales de l'Institut Henri Poincaré. Analyse Non Linéaire 26 (1): 159–180, doi:10.1016/j.anihpc.2007.10.002, ISSN 0294-1449, http://dx.doi.org/10.1016/j.anihpc.2007.10.002 

Kassmann, Moritz (2009), "A priori estimates for integro-differential operators with measurable kernels", Calculus of Variations and Partial Differential Equations 34 (1): 1–21, doi:10.1007/s00526-008-0173-6, ISSN 0944-2669, http://dx.doi.org/10.1007/s00526-008-0173-6 

Kiselev, A.; Nazarov, F. (2009), "A variation on a theme of Caffarelli and Vasseur", Rossiĭskaya Akademiya Nauk. Sankt-Peterburgskoe Otdelenie. Matematicheski\u\i Institut im. V. A. Steklova. Zapiski Nauchnykh Seminarov (POMI) 370: 58–72, ISSN 0373-2703 

2008

Barles, G.; Chasseigne, Emmanuel; Imbert, Cyril (2008), "On the Dirichlet problem for second-order elliptic integro-differential equations", Indiana University Mathematics Journal 57 (1): 213–246, doi:10.1512/iumj.2008.57.3315, ISSN 0022-2518, http://dx.doi.org/10.1512/iumj.2008.57.3315 

Barles, Guy; Imbert, Cyril (2008), "Second-order elliptic integro-differential equations: viscosity solutions' theory revisited", Annales de l'Institut Henri Poincaré. Analyse Non Linéaire 25 (3): 567–585, doi:10.1016/j.anihpc.2007.02.007, ISSN 0294-1449, http://dx.doi.org/10.1016/j.anihpc.2007.02.007 

Caffarelli, Luis; Salsa, Sandro; Silvestre, Luis (2008), "Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian", Inventiones Mathematicae 171 (2): 425–461, doi:10.1007/s00222-007-0086-6, ISSN 0020-9910, http://dx.doi.org/10.1007/s00222-007-0086-6 

2007

Bogdan, Krzysztof; Jakubowski, Tomasz (2007), "Estimates of heat kernel of fractional Laplacian perturbed by gradient operators", Communications in Mathematical Physics 271 (1): 179–198, doi:10.1007/s00220-006-0178-y, ISSN 0010-3616, http://dx.doi.org/10.1007/s00220-006-0178-y 

Caffarelli, Luis; Silvestre, Luis (2007), "An extension problem related to the fractional Laplacian", Communications in Partial Differential Equations 32 (7): 1245–1260, doi:10.1080/03605300600987306, ISSN 0360-5302, http://dx.doi.org.ezproxy.lib.utexas.edu/10.1080/03605300600987306 

Forcadel, N.; Lio, F.; Cardaliaguet, P.; Monneau, Régis (2007), "Dislocation dynamics: a non-local moving boundary", Free boundary problems (Berlin, New York: Springer-Verlag): 125–135 

2005

Bass, Richard F.; Kassmann, Moritz (2005), "Harnack inequalities for non-local operators of variable order", Transactions of the American Mathematical Society 357 (2): 837–850, doi:10.1090/S0002-9947-04-03549-4, ISSN 0002-9947, http://dx.doi.org/10.1090/S0002-9947-04-03549-4 

2002

Bass, Richard F.; Levin, David A. (2002), "Harnack inequalities for jump processes", Potential Analysis. An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis 17 (4): 375–388, doi:10.1023/A:1016378210944, ISSN 0926-2601, http://dx.doi.org/10.1023/A:1016378210944 

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