PUBLICATIONS



[299] Caffarelli, L.; De Silva, D.; Savin, O. The two membranes problem for different operators. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 4, 899--932.

[298] Caffarelli, Luis; Ros-Oton, Xavier; Serra, Joaquim. Obstacle problems for integro-differential operators: regularity of solutions and free boundaries. Invent. Math. 208 (2017), no. 3, 1155--1211.

[297] Caffarelli, Luis A.; Sire, Yannick. On some pointwise inequalities involving nonlocal operators. Harmonic analysis, partial differential equations and applications, 1--18, Appl. Numer. Harmon. Anal., Birkhäuser/Springer, Cham, 2017.

[296] Allen, Mark; Caffarelli, Luis; Vasseur, Alexis. Porous medium flow with both a fractional potential pressure and fractional time derivative. Chin. Ann. Math. Ser. B 38 (2017), no. 1, 45--82.

[295] Caffarelli, Luis; Dipierro, Serena; Valdinoci, Enrico. A logistic equation with nonlocal interactions. Kinet. Relat. Models 10 (2017), no. 1, 141--170.

[294] Caffarelli, Luis; Vázquez, Juan Luis. Regularity of solutions of the fractional porous medium flow with exponent ½. St. Petersburg Math. J. 27 (2016), 437--460.

[293] Arapostathis, Ari; Biswas, Anup; Caffarelli, Luis. The Dirichlet problem for stable-like operators and related probabilistic representations. Comm. Partial Differential Equations. 41 (2016), no. 9, 1472--1511.

[292] Caffarelli, L.; De Silva, D.; Savin, O. Obstacle-type problems for minimal surfaces. Comm. Partial Differential Equations 41 (2016), no. 8, 1303--1323.

[291] Caffarelli, Luis A.; Kriventsov, Dennis. A free boundary problem related to thermal insulation. Comm. Partial Differential Equations 41 (2016), no. 7, 1149--1182.

[290] Caffarelli, Luis; Silvestre, Luis. A nonlocal Monge-Ampère equation. Comm. Anal. Geom. 24 (2016), no. 2, 307--335.

[289] Caffarelli, Luis; Stinga, Pablo Raúl Fractional elliptic equations, Caccioppoli estimates and regularity. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2015), no. 3, 767--807.

[288] Allen, Mark; Caffarelli, Luis; Vasseur, Alexis. A Parabolic Problem with a Fractional-Time Derivative. Arch. Ration. Mech. Anal. 221 (2016), no. 2, 603--630.

[287] Bonforte, Matteo; Caffarelli, Luis; Grillo, Gabriele. Foreword. Nonlinear Anal. 137/138 (2016), 1--2.

[286] Caffarelli, Luis; Charro, Fernando. On a fractional Monge-Ampère operator. Annals of PDE 1 (2015), no. 1, 1--47.

[285] Caffarelli, Luis A.; Wang, Peiyong. A bifurcation phenomenon in a singularly perturbed one-phase free boundary problem of phase transition. Calc. Var. Partial Differential Equations 54 (2015), no. 4, 3517--3529.

[284] Caffarelli, Luis A.; Shahgholian, Henrik. Regularity of free boundaries a heuristic retro. Philos. Trans. A 373 (2015), no. 2050, 20150209, 18 pp.

[283] Caffarelli, Luis; Savin, Ovidiu; Valdinoci, Enrico. Minimization of a fractional perimeter-Dirichlet integral functional. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 32 (2015), no. 4, 901--924.

[282] Caffarelli, Luis; Silvestre, Luis. Hölder regularity for generalized master equations with rough kernels. Advances in analysis: the legacy of Elias M. Stein (C. Fefferman, A.D. Ionescu, D.H. Phong and S. Wainger, Eds.) Princeton University Press, Princeton, NJ (2014) 63--83.

[281] Caffarelli, Luis. Calixto Calderón as I knew him. Special functions, partial differential equations, and harmonic analysis, 13--14, Springer Proc. Math. Stat., 108 Springer, Cham, 2014.

[280] Caffarelli, Luis A.; Leitão, Raimundo; Urbano, José Miguel Regularity for anisotropic fully nonlinear integro-differential equations. Math. Ann. 360 (2014), no. 3-4, 681--714.

[279] Burger, Martin; Caffarelli, Luis; Markowich, Peter A. Partial differential equation models in the socio-economic sciences. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 372 (2014), no. 2028, 91--06.

[278] Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese On the asymptotic behavior of a Boltzmann-type price formation model. Commun. Math. Sci. 12 (2014), no. 7, 1353--1361.

[277] Caffarelli, Luis; Jin, Tianling; Sire, Yannick; Xiong, Jingang Local Analysis of Solutions of Fractional Semi-Linear Elliptic Equations with Isolated Singularities. Arch. Ration. Mech. Anal. 213 (2014), no. 1, 245--268.

[276] Caffarelli, Luis A.; Crandall, Michael G. Relations between geometric convexity, doubling measures and property Γ. Proc. Amer. Math. Soc. 142 (2014), no. 7, 2395--2406.

[275] Caffarelli, Luis A.; Monneau, Regis Counter-example in three dimension and homogenization of geometric motions in two dimension. Arch. Ration. Mech. Anal. 211 (2014) no. 2, 503--574.

[274] Caffarelli, Luis; González, María del Mar; Nguyen, Truyen A perturbation argument for a Monge-Ampère type equation arising in optimal transportation. Arch. Ration. Mech. Anal. 212 (2014), 359--414.

[273] Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese On a Boltzmann-type price formation model. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 469 (2013), no. 2157.

[272] Caffarelli, Luis The homogenization of surfaces and boundaries. Bull. Braz. Math. Soc. (N.S.) 44 (2013) no. 4, 755--775.

[271] Caffarelli, Luis; Valdinoci, Enrico Regularity properties of nonlocal minimal surfaces via limiting arguments. Adv. Math. 248 (2013), 843--871.

[270] Caffarelli, Luis; Figalli, Alessio Regularity of solutions to the parabolic fractional obstacle problem. J. Reine Angew. Math. 680 (2013), 191--233.

[269] Caffarelli, Luis; Soria, Fernando; Vázquez, Juan Luis Regularity of solutions of the fractional porous medium flow. J. Eur. Math. Soc. (JEMS) 15 (2013), no. 5, 1701--1746.

[268] Caffarelli, Luis; Valdinoci, Enrico A priori bounds for solutions of a nonlocal evolution PDE. Analysis and numerics of partial differential equation 141--163, Springer INdAM Ser. 4, Springer, Milan, 2013.

[267] Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis Some remarks on singular solutions of nonlinear elliptic equations III: viscosity solutions including parabolic operators. Comm. Pure Appl. Math. 66 (2013), no. 1, 109--143.

[266] Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis Some remarks on singular solutions of nonlinear elliptic equations II: Symmetry and monotonicity via moving planes. Advances in geometric analysis, 97--105, Adv. Lect. Math. (ALM), 21 Int. Press, Somerville, MA, 2012.

[265] Caffarelli, Luis A.; Golse, Francois; Guo, Yan; Kenig, Carlos E.; Vasseur, Alexis Nonlinear partial differential equations. Selected lecture notes from the School "Topics in PDE's and Applications 2008. A CRM & FISYMAT Joint Activity" held at the Universidad de Granada, Granada, April 7--11 and at the Centre de Recerca Matemàtica in Bellaterra, May 5--9, 2008. Edited by Xavier Cabré and Juan Soler. Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser/Springer Basel AG, Basel, 2012. viii+149 pp.

[264] Caffarelli, Luis A.; Vasseur, Alexis The De Giorgi method for nonlocal fluid dynamics. Nonlinear partial differential equations, 1--38, Adv. Courses Math. CRM Barcelona, Birkhäuser/Springer Basel AG, Basel, 2012.

[263] Caffarelli, Luis Non local diffusions, drifts and games. Nonlinear Partial Differential Equations: The Abel Symposium 2010. Series: Abel Symposia (H. Holden, K.H. Karlsen, Eds.) 7 Springer-Verlag, Berlin Heidelberg (2012) 37--52.

[262] Bjorland, C.; Caffarelli, L.; Figalli, A. Non-local gradient dependent operators. Adv. Math. 230 (2012), no. 4-6, 1859--1894.

[261] Caffarelli, L.; Mellet, A.; Sire, Y. Traveling waves for a boundary reaction-diffusion equation. Adv. Math. 230 (2012), no. 2, 433--457.

[260] Caffarelli, Luis A.; Crandall, Michael G. The problem of two sticks. Expo. Math. 30 (2012), no. 1, 69--95.

[259] Bjorland, C.; Caffarelli, L.; Figalli, A. Nonlocal tug-of-war and the infinity fractional Laplacian. Comm. Pure Appl. Math. 65 (2012), no. 3, 337--380.

[258] Caffarelli, Luis; Vázquez, Juan Luis Nonlinear porous medium flow with fractional potential pressure. Arch. Ration. Mech. Anal. 202 (2011), no. 2, 537--565.

[257] Ambrosio, Luigi; Caffarelli, Luis; Maugeri, Antonino Preface: A beautiful walk in the way of the understanding. Discrete Contin. Dyn. Syst. 31 (2011), no. 4, i--vi.

[256] Caffarelli, Luis; Silvestre, Luis The Evans-Krylov theorem for nonlocal fully nonlinear equations. Ann. of Math. (2) 174 (2011), no. 2, 1163--1187.

[255] Caffarelli, Luis A.; Markowich, Peter A.; Wolfram, Marie-Therese On a price formation free boundary model by Lasry and Lions: the Neumann problem. C. R. Math. Acad. Sci. Paris 349 (2011), no. 15-16, 841--844.

[254] Caffarelli, Luis A.; Markowich, Peter A.; Pietschmann, Jan-F. On a price formation free boundary model by Lasry and Lions. C. R. Math. Acad. Sci. Paris 349 (2011), no. 11-12, 621--624.

[253] Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis Regularity theory for parabolic nonlinear integral operators. J. Amer. Math. Soc. 24 (2011), no. 3, 849--869.

[252] Caffarelli, Luis; Valdinoci, Enrico Uniform estimates and limiting arguments for nonlocal minimal surfaces. Calc. Var. Partial Differential Equations 41 (2011), no. 1-2, 203--240.

[251] Caffarelli, Luis; Silvestre, Luis Regularity results for nonlocal equations by approximation. Arch. Ration. Mech. Anal. 200 (2011), no. 1, 59--88.

[250] Caffarelli, Luis A.; Vázquez, Juan Luis Asymptotic behaviour of a porous medium equation with fractional diffusion. Discrete Contin. Dyn. Syst. 29 (2011), no. 4, 1393--1404.

[249] Caffarelli, Luis; Li, YanYan Preface [Special issue dedicated to Louis Nirenberg on the occasion of his 85th birthday. Part III]. Discrete Contin. Dyn. Syst. 30 (2011), no. 2, i--ii.

[248] Caffarelli, Luis A.; Crandall, Michael G. Distance functions and almost global solutions of eikonal equations. Comm. Partial Differential Equations 35 (2010), no. 3, 391--414.

[247] Caffarelli, Luis; Silvestre, Luis Smooth approximations of solutions to nonconvex fully nonlinear elliptic equations. Nonlinear partial differential equations and related topics, 67--85, Amer. Math. Soc. Transl. Ser. 2, 229, Amer. Math. Soc., Providence, RI, 2010.

[246] Caffarelli, Luis A.; Vasseur, Alexis F. The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. Discrete Contin. Dyn. Syst. Ser. S 3 (2010), no. 3, 409--427.

[245] Caffarelli, Luis A.; Vasseur, Alexis Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Ann. of Math. (2) 171 (2010), no. 3, 1903--1930.

[244] Caffarelli, Luis A.; Roquejoffre, Jean-Michel; Sire, Yannick Variational problems for free boundaries for the fractional Laplacian. J. Eur. Math. Soc. (JEMS) 12 (2010), no. 5, 1151--1179.

[243] Caffarelli, L.; Roquejoffre, J.-M.; Savin, O. Nonlocal minimal surfaces. Comm. Pure Appl. Math. 63 (2010), no. 9, 1111--1144.

[242] Caffarelli, Luis A.; Lin, Fang Hua Analysis on the junctions of domain walls. Discrete Contin. Dyn. Syst. 28 (2010) no. 3, 915--929.

[241] Caffarelli, Luis A.; Li, YanYan Preface [Dedicated to Louis Nirenberg on the occasion of his 85th birthday. Part I]. Discrete Contin. Dyn. Syst. 28 (2010) no. 2, i--ii.

[240] Caffarelli, Luis A.; Li, YanYan Preface [Dedicated to Louis Nirenberg on the occasion of his 85th birthday. Part II]. Discrete Contin. Dyn. Syst. 28 (2010) no. 3, i--ii.

[239] Caffarelli, Luis A.; McCann, Robert J. Free boundaries in optimal transport and Monge-Ampère obstacle problems. Ann. of Math. (2) 171 (2010), no. 2, 673--730.

[238] Caffarelli, Luis A.; Souganidis, Panagiotis E. Rates of convergence for the homogenization of fully nonlinear uniformly elliptic pde in random media. Invent. Math. 180 (2010), no. 2, 301--360.

[237] Athanasopoulos, I.; Caffarelli, L. A. Continuity of the temperature in boundary heat control problems. Adv. Math. 224 (2010), no. 1, 293--315.

[236] Caffarelli, Luis A.; Karakhanyan, Aram L. Lectures on gas flow in porous media. Recent developments in real and harmonic analysis, 133--157, Appl. Numer. Harmon. Anal., Birkhäuser Boston, Inc., Boston, MA, 2010.

[235] Caffarelli, Luis A.; Souganidis, Panagiotis E. Convergence of nonlocal threshold dynamics approximations to front propagation. Arch. Ration. Mech. Anal. 195 (2010), no. 1, 1--23.

[234] Caffarelli, Luis; Silvestre, Luis On the Evans-Krylov theorem. Proc. Amer. Math. Soc. 138 (2010), no. 1, 263--265.

[233] Caffarelli, Luis A. Some nonlinear problems involving non-local diffusions. ICIAM 07: 6th International Congress on Industrial and Applied Mathematics, 43--56, Eur. Math. Soc., Zurich, 2009.

[232] Caffarelli, Luis Surfaces minimizing nonlocal energies. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 20 (2009), no. 3, 281--299.

[231] Caffarelli, Luis; Li, Yan Yan; Nirenberg, Louis Some remarks on singular solutions of nonlinear elliptic equations. I. J. Fixed Point Theory Appl. 5 (2009), no. 2, 353--395.

[230] Caffarelli, L. A.; Karakhanyan, A. L.; Lin, Fang-Hua The geometry of solutions to a segregation problem for nondivergence systems. J. Fixed Point Theory Appl., 5 (2009), no. 2, 319--351.

[229] Caffarelli, Luis A.; Huang, Qingbo Reflector problem in ${\Bbb R}^n$ endowed with non-Euclidean norm. Arch. Ration. Mech. Anal. 193 (2009), no. 2, 445--473.

[228] Caffarelli, L. A.; Mellet, A. Random homogenization of an obstacle problem. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 2, 375--395.

[227] Caffarelli, Luis; Silvestre, Luis Regularity theory for fully nonlinear integro-differential equations. Comm. Pure Appl. Math. 62 (2009), no. 5, 597--638.

[226] Caffarelli, Luis; Lin, Fanghua Nonlocal heat flows preserving the $L^2$ energy. Discrete Contin. Dyn. Syst. 23 (2009), no. 1-2, 49--64.

[225] Caffarelli, L. A.; Oliker, V. I. Weak solutions of one inverse problem in geometric optics. Problems in mathematical analysis. No. 37. J. Math. Sci. (N. Y.) 154 (2008), no. 1, 39--49.

[224] Caffarelli, L. A.; Glowinski, R. Numerical solution of the Dirichlet problem for a Pucci equation in dimension two. Application to homogenization. J. Numer. Math. 16 (2008), no. 3, 185--216.

[223] Caffarelli, Luis A.; Stefanelli, Ulisse A counterexample to $C^{2,1}$ regularity for parabolic fully nonlinear equations. Comm. Partial Differential Equations 33 (2008), no. 7-9, 1216--1234.

[222] Caffarelli, Luis; Lee, Ki-ahm Viscosity method for homogenization of highly oscillating obstacles. Indiana Univ. Math. J. 57 (2008), no. 4, 1715--1741.

[221] Caffarelli, Luis; Mellet, Antoine Random homogenization of fractional obstacle problems. Netw. Heterog. Media 3 (2008), no. 3, 523--554.

[220] Caffarelli, Luis; Silvestre, Luis Issues in homogenization for problems with non divergence structure. Calculus of variations and nonlinear partial differential equations, 43--74, Lecture Notes in Math., 1927, Springer, Berlin, 2008.

[219] Ambrosio, Luigi; Caffarelli, Luis; Crandall, Michael G.; Evans, Lawrence C.; Fusco, Nicola Calculus of variations and nonlinear partial differential equations. Lectures given at the C. I. M. E. Summer School held in Cetraro, June 27--July 2, 2005. With a historical overview of C. I. M. E. courses on the topic by Elvira Mascolo. Edited by Bernard Dacorogna and Paolo Marcellini. Lecture Notes in Mathematics, 1927. Springer-Verlag, Berlin; Fondazione C.I.M.E., Florence, 2008. xxii+196 pp. ISBN 978-3-540-75913-3

[218] Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S. The structure of the free boundary for lower dimensional obstacle problems. Amer. J. Math. 130 (2008), no. 2, 485--498.

[217] Caffarelli, L. A.; Lin, Fang-Hua Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. J. Amer. Math. Soc. 21 (2008), no. 3, 847--862.

[216] Caffarelli, Luis A.; Gutiérrez, Cristian E.; Huang, Qingbo On the regularity of reflector antennas. Ann. of Math. (2) 167 (2008), no. 1, 299--323.

[215] Caffarelli, Luis A.; Salsa, Sandro; Silvestre, Luis Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Invent. Math. 171 (2008), no. 2, 425--461.

[214] Caffarelli, Luis A.; Souganidis, Panagiotis E. A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs. Comm. Pure Appl. Math. 61 (2008), no. 1, 1--17.

[213] Caffarelli, Luis Free boundary problems for fractional powers of the Laplacian. A great mathematician of the nineteenth century. Papers in honor of Eugenio Beltrami (1835--1900) (Italian), 273--286, Ist. Lombardo Accad. Sci. Lett. Incontr. Studio, 39, LED--Ed. Univ. Lett. Econ. Diritto, Milan, 2007.

[212] Caffarelli, L. A.; Mellet, A. Capillary drops on an inhomogeneous surface. Perspectives in nonlinear partial differential equations,, 175--201, Contemp. Math., 446, Amer. Math. Soc., Providence, RI, 2007.

[211] Caffarelli, Luis; Guan, Pengfei; Ma, Xi-Nan A constant rank theorem for solutions of fully nonlinear elliptic equations. Comm. Pure Appl. Math. 60 (2007), no. 12, 1769--1791.

[210] Caffarelli, Luis; Silvestre, Luis An extension problem related to the fractional Laplacian. Comm. Partial Differential Equations 32 (2007), no. 7-9, 1245--1260.

[209] Caffarelli, L. A.; Lin, Fang Hua An optimal partition problem for eigenvalues. J. Sci. Comput. 31 (2007), no. 1-2, 5--18.

[208] Caffarelli, L. A.; Mellet, A. Capillary drops: contact angle hysteresis and sticking drops. Calc. Var. Partial Differential Equations 29 (2007), no. 2, 141--160.

[207] Caffarelli, L.; Lee, K. Homogenization of oscillating free boundaries: the elliptic case. Comm. Partial Differential Equations 32 (2007), no. 1-3, 149--162.

[206] Caffarelli, L. A.; Lee, K.-A.; Mellet, A. Flame propagation in one-dimensional stationary ergodic media. Math. Models Methods Appl. Sci. 17 (2007), no. 1, 155--169.

[205] Caffarelli, Luis A.; Roquejoffre, Jean-Michel Uniform Hölder estimates in a class of elliptic systems and applications to singular limits in models for diffusion flames. Arch. Ration. Mech. Anal. 183 (2007), no. 3, 457--487.

[204] Caffarelli, Luis A homogenization method for non variational problems. Current developments in mathematics, 2004, 73--93, Int. Press, Somerville, MA, 2006.

[203] Caffarelli, Luis; Manasevich, Raul; Rodrigues, Hildebrando; Yi, Yingfei Preface [Pan-American Advanced Studies Institute on Differential Equations and Nonlinear Analysis]. Held in Santiago, January 10--21, 2005. J. Dynam. Differential Equations 18 (2006), no. 3, 483--484.

[202] Caffarelli, L.; Li, YanYan Some multi-valued solutions to Monge-Ampère equations. Comm. Anal. Geom. 14 (2006), no. 3, 411--441.

[201] Caffarelli, Luis A.; Córdoba, Antonio Phase transitions: uniform regularity of the intermediate layers. J. Reine Angew. Math. 593 (2006), 209--235.

[200] Caffarelli, Luis A.; Wang, Lihe A Harnack inequality approach to the interior regularity gradient estimates of geometric equations. J. Partial Differential Equations 19 (2006), no. 1, 16--25.

[199] Caffarelli, L. A.; Lee, K.-A.; Mellet, A. Homogenization and flame propagation in periodic excitable media: the asymptotic speed of propagation. Comm. Pure Appl. Math. 59 (2006), no. 4, 501--525.

[198] Caffarelli, L.; Lee, Ki-Ahm Homogenization of nonvariational viscosity solutions. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5) 29 (2005), no. 1, 89--100.

[197] Caffarelli, Luis; Salsa, Sandro A geometric approach to free boundary problems. Graduate Studies in Mathematics, 68 American Mathematical Society, Providence, RI. 2005. x+270 pp. ISBN: 0-8218-3784-2

[196] Caffarelli, Luis A.; de la Llave, Rafael Interfaces of ground states in Ising models with periodic coefficients. J. Stat. Phys. 118 (2005), no. 3-4, 687--719.

[195] Caffarelli, Luis A.; Souganidis, Panagiotis E.; Wang, L. Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media. Comm. Pure Appl. Math. 58 (2005), no. 3, 319--361.

[194] Caffarelli, L. A.; Shahgholian, H. The structure of the singular set of a free boundary in potential theory. Izv. Nats. Akad. Nauk Armenii Mat. 39 (2004), no. 2, 43--58; translation in J. Contemp. Math. Anal. 39 (2004), no. 2, 2--20 (2005)

[193] Athanasopoulos, I.; Caffarelli, L. A. Optimal regularity of lower dimensional obstacle problems. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 310 (2004), Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funkts. 35 [34], 49--66, 226; translation in J. Math. Sci. (N. Y.) 132 (2006), no. 3, 274--284.

[192] Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E. Global energy minimizers for free boundary problems and full regularity in three dimensions. Noncompact problems at the intersection of geometry, analysis, and topology, 83--97, Contemp. Math., 350, Amer. Math. Soc., Providence, RI, 2004.

[191] Caffarelli, Luis; Petrosyan, Arshak; Shahgholian, Henrik Regularity of a free boundary in parabolic potential theory. J. Amer. Math. Soc. 17 (2004), no. 4, 827--869. (electronic).

[190] Caffarelli, Luis A. The Monge Ampère equation and optimal transportation. Recent advances in the theory and applications of mass transport, 43--52, Contemp. Math. 353,Amer. Math. Soc., Providence, RI, 2004.

[189] Caffarelli, Luis A.; Lee, Ki-Ahm; Mellet, Antoine Singular limit and homogenization for flame propagation in periodic excitable media. Arch. Ration. Mech. Anal. 172 (2004), no. 2, 153--190.

[188] Caffarelli, L.; Li, Yan Yan A Liouville theorem for solutions of the Monge-Ampère equation with periodic data. Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004), no. 1, 97--120.

[187] Caffarelli, Luis; Salazar, Jorge; Shahgholian, Henrik Free-boundary regularity for a problem arising in superconductivity. Arch. Ration. Mech. Anal. 171 (2004), no. 1, 115--128.

[186] Caffarelli, Luis Some Liouville theorems for PDE problems in periodic media. Renato Caccioppoli and modern analysis. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 14 (2003), no. 3, 247--256 (2004).

[185] Caffarelli, Luis The Monge-Ampère equation and optimal transportation, an elementary review. Optimal transportation and applications (Martina Franca, 2001), 1--10, Lecture Notes in Math. 1813 Springer, Berlin, 2003.

[184] Ambrosio, L.; Caffarelli, L. A.; Brenier, Y.; Buttazzo, G.; Villani, C. Optimal transportation and applications. Lectures from the C.I.M.E. Summer School held in Martina Franca, September 2--8, 2001. Edited by Caffarelli and S. Salsa. Lecture Notes in Mathematics, 1813. Springer-Verlag, Berlin, Centro Internazionale Matematico Estivo (C.I.M.E.), Florence, 2003. viii+164 pp. ISBN: 3-540-40192-X

[183] Cabré, Xavier; Caffarelli, Luis A. Interior $C^{2,\alpha}$ regularity theory for a class of nonconvex fully nonlinear elliptic equations. J. Math. Pures Appl. (9) 82 (2003), no. 5, 573--612.

[182] Caffarelli, Luis A.; Huang, Qingbo Estimates in the generalized Campanato-John-Nirenberg spaces for fully nonlinear elliptic equations. Duke Math. J. 118 (2003), no. 1, 1--17.

[181] Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S. Stefan-like problems with curvature. J. Geom. Anal. 13 (2003), no. 1, 21--27.

[180] Caffarelli, L.; Li, YanYan An extension to a theorem of Jörgens, Calabi, and Pogorelov. Comm. Pure Appl. Math. 56 (2003), no. 5, 549--583.

[179] Caffarelli, Luis A. Non linear elliptic theory and the Monge-Ampere equation. Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002), 179--187, Higher Ed. Press, Beijing, 2002.

[178] Caffarelli,Luis A.; Jerison, David; Kenig, Carlos E. Some new monotonicity theorems with applications to free boundary problems. Ann. of Math. (2) 155 (2002), 369--404

[177] Caffarelli,Luis A.; Roquejoffre, Jean-Michel A nonlinear oblique derivative boundary value problem for the heat equation: analogy with the porous medium equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 19 (2002), no. 1, 41--80.

[176] Caffarelli, L.; Salazar, J. Solutions of fully nonlinear elliptic equations with patches of zero gradient: existence, regularity and convexity of level curves. Trans. Amer. Math. Soc. 354 (2002), no. 8, 3095--3115 (electronic).

[175] Caffarelli, Luis A. Erratum: "Monotonicity of optimal transportation and the FKG and related inequalities'' [Comm. Math. Phys. 214 (2000), no. 3, 547--563; Comm. Math. Phys. 225 (2002), no. 2, 449--450.

[174] Caffarelli, Luis A.; Feldman, Mikhail; McCann, Robert J. Constructing optimal maps for Monge's transport problem as a limit of strictly convex costs. J. Amer. Math. Soc. 15 (2002), no. 1, 1--26 (electronic).

[173] Cabré, Xavier; Caffarelli, Luis A. Regularity theory for a class of nonconvex fully nonlinear elliptic equations. XVII CEDYA: Congress on Differential Equations and Applications/VII CMA: Congress on Applied Mathematics (Spanish) (Salamanca, 2001), 57--62, Dep. Mat. Apl., Univ. Salamanca, Salamanca, 2001.

[172] Caffarelli, Luis A.; Viaclovsky, Jeff A. On the regularity of solutions to Monge-Ampère equations on Hessian manifolds. Comm. Partial Differential Equations 26 (2001), no. 11-12, 2339--2351.

[171] Caffarelli, Luis A.; de la Llave, Rafael Planelike minimizers in periodic media. Comm. Pure Appl. Math. 54 (2001), no. 12, 1403--1441.

[170] Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S. The free boundary in an inverse conductivity problem. J. Reine Angew. Math. 534 (2001), 1--31.

[169] Athanasopoulos, I.; Caffarelli, L. A.; Kenig, C.; Salsa, S. An area-Dirichlet integral minimization problem. Comm. Pure Appl. Math 54 (2001), no. 4, 479--499.

[168] Caffarelli, Luis A. Monotonicity properties of optimal transportation and the FKG and related inequalities. Comm. Math. Phys. 214 (2000), no. 3, 547--563.

[167] Caffarelli, Luis A.; Yuan, Yu A priori estimates for solutions of fully nonlinear equations with convex level set. Indiana Univ. Math. J. 49 (2000), no. 2, 681--695.

[166] Caffarelli, Luis; Dolbeault, Jean; Markowich, Peter A.; Schmeiser, Christian On Maxwellian equilibria of insulated semiconductors. Interfaces Free Bound. 2 (2000), no. 3, 331--339.

[165] Caffarelli, Luis A.; Karp, Lavi; Shahgholian, Henrik Regularity of a free boundary with application to the Pompeiu problem. Ann. of Math. (2) 151 (2000), no. 1, 269--292.

[164] Caffarelli, Luis A. The Monge Ampère equation, allocation problems, and elliptic systems with affine invariance. Harmonic analysis and partial differential equations (Chicago, IL, 1996), 117--126, Chicago Lectures in Math., Univ. Chicago Press, Chicago, IL, 1999.

[163] Caffarelli, Luis A. The Harnack inequality and non-divergence equations. Nonlinear partial differential equations (Evanston, IL, 1998), 27--34, Contemp. Math. 238, Amer. Math. Soc., Providence, RI, 1999.

[162] Caffarelli, L. A. A note on nonlinear homogenization. Comm. Pure Appl. Math. 52 (1999), no. 7, 829--838.

[161] Caffarelli, Luis; Vázquez, Juan Luis Viscosity solutions for the porous medium equation. Differential equations: La Pietra 1996 (Florence), 13--26, Proc. Sympos. Pure Math. 65, Amer. Math. Soc., Providence, RI, 1999.

[160] Caffarelli, Luis A.; Milman, Mario, Eds. Monge Ampère equation: applications to geometry and optimization. 1999 Proceedings of the NSF-CBMS Conference held at Florida Atlantic University, Deerfield Beach, FL, July 9-13, 1997. x+172 pp. Contemp. Math. 226 Amer. Math. Soc., Providence, RI, 1999.

[159] Caffarelli, Luis A.; Kochengin, Sergey A.; Oliker, Vladimir I. On the numerical solution of the problem of reflector design with given far-field scattering data. Monge Ampère equation: applications to geometry and optimization (Deerfield Beach, FL, 1997), 13--32, Contemp. Math. 226, Amer. Math. Soc., Providence, RI, 1999.

[158] Caffarelli, Luis A.; E, Weinan, Eds. Hyperbolic equations and frequency interactions. Lectures from the Graduate Summer School on Nonlinear Wave Phenomena, Park City, UT, July 9--29, 1995. xii+466 pp. Park City Mathematics Series 5 IAS, 1999.

[157] Caffarelli, Luis A. The obstacle problem. Lezioni Fermiane. [Fermi Lectures] Accademia Nazionale dei Lincei, Rome; Scuola Normale Superiore, Pisa, 1998. ii+54 pp.

[156] Caffarelli, L. A. The obstacle problem revisited. J. Fourier Anal. Appl. 4 (1998), no. 4-5, 383--402.

[155] Caffarelli, Luis A.; Kenig, Carlos E. Gradient estimates for variable coefficient parabolic equations and singular perturbation problems. Amer. J. Math. 120 (1998), no. 2, 391--439.

[154] Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S. Phase transition problems of parabolic type: flat free boundaries are smooth. Comm. Pure Appl. Math. 51 (1998), no. 1, 77--112.

[153] Caffarelli, L. A.; Peral, I. On $W^{1,p}$ estimates for elliptic equations in divergence form. Comm. Pure Appl. Math. 51 (1998), no. 1, 1--21.

[152] Berestycki, Henri; Caffarelli, Luis; Nirenberg, Louis Further qualitative properties for elliptic equations in unbounded domains. Dedicated to Ennio De Giorgi. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997), no. 1-2, 69--94.

[151] Caffarelli, Luis The work of Jean Bourgain [see MR1403907 (97c:00049)]. Fields Medallists' lectures, 537--539, World Sci. Ser. 20th Century Math. 5, World Sci. Publ., River Edge, NJ, 1997.

[150] Caffarelli, L. A.; Lederman, C.; Wolanski, N. Pointwise and viscosity solutions for the limit of a two phase parabolic singular perturbation problem. Indiana Univ. Math. J. 46 (1997), no. 3, 719--740.

[149] Caffarelli, L. A.; Lederman, C.; Wolanski, N. Uniform estimates and limits for a two phase parabolic singular perturbation problem. Indiana Univ. Math. J., 46 (1997), no. 2, 453--489.

[148] Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. Monotonicity for elliptic equations in unbounded Lipschitz domains. Comm. Pure Appl. Math. 50 (1997), no. 11, 1089--1111.

[147] Caffarelli, Luis A.; Gutiérrez, Cristian E. Singular integrals related to the Monge-Ampère equation. Wavelet theory and harmonic analysis in applied sciences (Buenos Aires, 1995), 3--13, Appl. Numer. Harmon. Anal. Birkhäuser Boston, Boston, MA, 1997.

[146] Caffarelli, Luis A. The regularity of monotone maps of finite compression. Comm. Pure Appl. Math. 50 (1997), no. 6, 563--591.

[145] Caffarelli, Luis A.; Gutiérrez, Cristian E. Properties of the solutions of the linearized Monge-Ampère equation. Amer. J. Math. 119 (1997), no. 2, 423--465.

[144] Caffarelli, Luis A. Boundary regularity of maps with convex potentials. II. Ann. of Math. (2) 144 (1996), no. 3, 453--496.

[143] Athanasopoulos, I.; Caffarelli, L.; Salsa, S. Regularity of the free boundary in parabolic phase-transition problems. Acta Math. 176 (1996), no. 2, 245--282.

[142] Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. Inequalities for second-order elliptic equations with applications to unbounded domains. I. A celebration of John F. Nash, Jr. Duke Math. J. 81 (1996), no. 2, 467--494.

[141] Athanasopoulos, I.; Caffarelli, L.; Salsa, S. Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems. Ann. of Math. (2) 143 (1996), no. 3, 413--434.

[140] Caffarelli, L.; Crandall, M. G.; Kocan, M.; Swiech, A. On viscosity solutions of fully nonlinear equations with measurable ingredients. Comm. Pure Appl. Math. 49 (1996), no. 4, 365--397.

[139] Caffarelli, Luis A.; Jerison, David; Lieb, Elliott H. On the case of equality in the Brunn-Minkowski inequality for capacity. Adv. Math. 117 (1996), no. 2, 193--207.

[138] Caffarelli, Luis A. Allocation maps with general cost functions. Partial differential equations and applications, 29--35, Lecture Notes in Pure and Appl. Math. 177 Dekker, New York, 1996.

[137] Caffarelli, Luis; Kohn, Joseph J. Louis Nirenberg receives National Medal of Science. With contributions by Luis Caffarelli and Joseph J. Kohn. Notices Amer. Math. Soc. 43 (1996) 1111--1116.

[136] Caffarelli, Luis A. A priori estimates and the geometry of the Monge-Ampère equation. Nonlinear partial differential equations in differential geometry (Park City, UT, 1992), 5--63, IAS/Park City Math. Ser., 2, Amer. Math. Soc., Providence, RI, 1996.

[135] Caffarelli, Luis A.; Gutiérrez, Cristian E. Real analysis related to the Monge-Ampère equation. Trans. Amer. Math. Soc. 348 (1996), no. 3, 1075--1092.

[134] Caffarelli, Luis The work of Jean Bourgain. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994) 3--5, Birkhäuser, Basel, 1995.

[133] Caffarelli, Luis A.; Cabré, Xavier Regularity for viscosity solutions of fully nonlinear equations $F(D^2u)=0$. Topol. Methods Nonlinear Anal. 6 (1995), no. 1, 31--48.

[132] Caffarelli, Luis A.; Muler, Nora E. An $L^\infty$ bound for solutions of the Cahn-Hilliard equation. Arch. Ration. Mech. Anal. 133 (1995), no. 2, 129--144.

[131] Caffarelli, Luis A.; Cabré, Xavier Fully nonlinear elliptic equations. American Mathematical Society Colloquium Publications, 43 American Mathematical Society, Providence, RI, 1995. vi+104 pp.

[130] Caffarelli, Luis A.; Milman, Mario The regularity of planar maps with bounded compression and rotation. Volume in homage to Dr. Rodolfo A. Ricabarra (Spanish), 29--34, Vol. Homenaje 1 Univ. Nac. del Sur, Bahía Blanca, 1995.

[129] Caffarelli, Luis A. Uniform Lipschitz regularity of a singular perturbation problem. Differential Integral Equations 8 (1995), no. 7, 1585--1590.

[128] Caffarelli, Luis A.; Yang, Yi Song Vortex condensation in the Chern-Simons Higgs model: an existence theorem. Comm. Math. Phys. 168 (1995), no. 2, 321--336.

[127] Caffarelli, Luis A.; Córdoba, Antonio Uniform convergence of a singular perturbation problem. Comm. Pure Appl. Math. 48 (1995), no. 1, 1--12.

[126] Caffarelli, Luis A.; Córdoba, Antonio Correction: "An elementary regularity theory of minimal surfaces" [Differential Integral Equations 6 (1993), no. 1, 1--13; MR1190161 (94c:49042)]. Differential Integral Equations 8 (1995), no. 1, 223.

[125] Caffarelli, Luis A.; Vázquez, Juan L. A free-boundary problem for the heat equation arising in flame propagation. Trans. Amer. Math. Soc. 347 (1995), no. 2, 411--441.

[124] Caffarelli, Luis; Garofalo, Nicola; Segàla, Fausto, A gradient bound for entire solutions of quasi-linear equations and its consequences. Comm. Pure Appl. Math. 47 (1994), no. 11, 1457--1473.

[123] Caffarelli, Luis A. A monotonicity formula for heat functions in disjoint domains. Boundary value problems for partial differential equations and applications 53--60, RMA Res. Notes Appl. Math. 29 Masson, Paris, 1993.

[122] Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. Symmetry for elliptic equations in a half space. Boundary value problems for partial differential equations and applications 27--42, RMA Res. Notes Appl. Math. 29 Masson, Paris, 1993.

[121] Caffarelli, Luis A. A note on the degeneracy of convex solutions to Monge Ampère equation. Comm. Partial Differential Equations 18 (1993), no. 7-8, 1213--1217.

[120] Caffarelli, Luis A.; Wang, Lihe A Harnack inequality approach to the interior regularity of parabolic equations. Indiana Univ. Math. J. 42 (1993), no. 1, 159--165.

[119] Caffarelli, Luis A.; Wang, Lihe A Harnack inequality approach to the interior regularity of elliptic equations. Indiana Univ. Math. J. 42 (1993), no. 1, 145--157.

[118] Caffarelli, Luis A.; Córdoba, Antonio An elementary regularity theory of minimal surfaces. Differential Integral Equations 6 (1993), no. 1, 1--13.

[117] Caffarelli, L. The regularity of mappings with convex potentials. Partial differential equations and related subjects (Trento, 1990) 53--58, Pitman Res. Notes Math. Ser. 269 Longman Sci. Tech., Harlow, 1992.

[116] Caffarelli, Luis A. Regularity of solutions and level surfaces of elliptic equations. American Mathematical Society centennial publications,Vol. II (Providence, RI, 1988) 7--13, Amer. Math. Soc., Providence, RI, 1992.

[115] Caffarelli, Luis A. Boundary regularity of maps with convex potentials. Comm. Pure Appl. Math. 45 (1992), no. 9, 1141--1151.

[114] Caffarelli, Luis A. The regularity of mappings with a convex potential. J. Amer. Math. Soc. 5 (1992), no. 1, 99--104.

[113] Caffarelli, Luis A. Some regularity properties of solutions of Monge-Ampère equation. Comm. Pure Appl. Math. 44 (1991), no. 8-9, 965--969

[112] Caffarelli, L. A. Free boundary problems and their singular perturbations. Frontiers in pure and applied mathematics, 43--46, North-Holland, Amsterdam, 1991.

[111] Caffarelli, Luis A.; Wolanski, Noemí I. $C^{1,\alpha}$ regularity of the free boundary for the $N$-dimensional porous media equation. Comm. Pure Appl. Math. 43 (1990), no. 7, 885--902.

[110] Caffarelli, Luis A. Interior regularity of solutions to Monge-Ampère equations. Harmonic analysis and partial differential equations (Boca Raton, FL, 1988), 13--17, Contemp. Math. 107 Amer. Math. Soc., Providence, RI, 1990.

[109] Caffarelli, Luis A.; Spruck, Joel Variational problems with critical Sobolev growth and positive Dirichlet data. Indiana Univ. Math. J. 39 (1990), no. 1, 1--18.

[108] Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. Uniform estimates for regularization of free boundary problems. Analysis and partial differential equations 567--619, Lecture Notes in Pure and Appl. Math. 122 Dekker, New York, 1990.

[107] Caffarelli, Luis A. Interior $W^{2,p}$ estimates for solutions of the Monge-Ampère equation. Ann. of Math. (2) 131 (1990), no. 1, 135--150.

[106] Caffarelli, L. A. A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity. Ann. of Math. (2) 131 (1990), no. 1, 129--134.

[105] Caffarelli, Luis A. Interior a priori estimates for solutions of fully nonlinear equations. Ann. of Math. (2) 130 (1989), no. 1, 189--213.

[104] Caffarelli, Luis A. Free boundary problems. A survey. Topics in calculus of variations (Montecatini Terme, 1987), 31--61, Lecture Notes in Math. 1365 Springer, Berlin, 1989.

[103] Caffarelli, L. A. A priori estimates for fully nonlinear second order elliptic equations. Nonlinear variational problems, Vol. II (Isola d'Elba, 1986), 99--106, Pitman Res. Notes Math. Ser. 193 Longman Sci. Tech., Harlow, 1989.

[102] Caffarelli, Luis A.; Gidas, Basilis; Spruck, Joel Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Comm. Pure Appl. Math. 42 (1989), no. 3, 271--297.

[101] Caffarelli, Luis A. A Harnack inequality approach to the regularity of free boundaries. II. Flat free boundaries are Lipschitz. Comm. Pure Appl. Math. 42 (1989), no. 1, 55--78.

[100] Caffarelli, Luis Elliptic second order equations. Rend. Sem. Mat. Fis. Milano 58 (1988), 253--284 (1990).

[99] Caffarelli, Luis A. A Harnack inequality approach to the regularity of free boundaries. III. Existence theory, compactness, and dependence on $X$. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (1988), no. 4, 583--602 (1989).

[98] Caffarelli, Luis A.; Friedman, Avner A model of dislocations and the associated free boundary problem. Indiana Univ. Math. J. 37 (1988), no. 3, 451--479.

[97] Caffarelli, L.; Nirenberg, L.; Spruck, J. On a form of Bernstein's theorem. Analyse mathématique et applications, 55--66, Gauthier-Villars, Montrouge, 1988.

[96] Caffarelli, Luis A.; Friedman, Avner Blowup of solutions of nonlinear heat equations. J. Math. Anal. Appl. 129 (1988), no. 2, 409--419.

[95] Caffarelli, Luis; Nirenberg, Louis; Spruck, Joel Nonlinear second-order elliptic equations. V. The Dirichlet problem for Weingarten hypersurfaces. Comm. Pure Appl. Math. 41 (1988), no. 1, 47--70.

[94] Caffarelli, Luis A. The differentiability of the free boundary for the $n$-dimensional porous media equation. Directions in partial differential equations (Madison, WI, 1985), 37--42, Publ. Math. Res. Center Univ. Wisconsin 54 Academic Press, Boston, MA, 1987.

[93] Caffarelli, Luis A. A Harnack inequality approach to the regularity of free boundaries. I. Lipschitz free boundaries are $C^{1,\alpha}$. Rev. Mat. Iberoamericana 3 (1987), no. 2, 139--162.

[92] Aguilera, N. E.; Caffarelli, L. A.; Spruck, J. An optimization problem in heat conduction. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 14 (1987), no. 3, 355--387 (1988).

[91] Caffarelli, Luis A.; Friedman, Avner Asymptotic behavior of solutions of $u_t=\Delta u^m$ as $m\to\infty$. Indiana Univ. Math. J. 36 (1987), no. 4, 711--728.

[90] Caffarelli, L.; Nirenberg, L.; Spruck, J. Correction to: "The Dirichlet problem for nonlinear second-order elliptic equations. I. Monge-Ampère equation" [Comm. Pure Appl. Math. 37 (1984), no. 3, 369--402; Comm. Pure Appl. Math. 40 (1987), no. 5, 659--662.

[89] Caffarelli, Luis A.; Friedman, Avner A singular perturbation problem for semiconductors. Boll. Un. Mat. Ital. B (7) 1 (1987), no. 2, 409--421.

[88] Caffarelli, L. A.; Vázquez, J. L.; Wolanski, N. I. Lipschitz continuity of solutions and interfaces of the $N$-dimensional porous medium equation. Indiana Univ. Math. J. 36 (1987), no. 2, 373--401.

[87] Caffarelli, L.; Nirenberg, L.; Spruck, J. Nonlinear second order elliptic equations. IV. Starshaped compact Weingarten hypersurfaces. Current topics in partial differential equations, 1--26, Kinokuniya, Tokyo, 1986.

[86] Aguilera, N. E.; Caffarelli, L. A. Regularity results for discrete solutions of second order elliptic problems in the finite element method. Calcolo 23 (1986), no. 4, 327--353 (1987).

[85] Aronson, D. G.; Caffarelli, L. A. Optimal regularity for one-dimensional porous medium flow. Rev. Mat. Iberoamericana 2 (1986), no. 4, 357--366.

[84] Caffarelli, L.; Nirenberg, L.; Spruck, J. The Dirichlet problem for the degenerate Monge-Ampère equation. Rev. Mat. Iberoamericana 2 (1986), no. 1-2, 19--27.

[83] Caffarelli, Luis A. A Harnack inequality approach to the regularity of free boundaries. Frontiers of the mathematical sciences: 1985 (New York, 1985). Comm. Pure Appl. Math. 39 (1986), no. S, suppl., S41--S45.

[82] Caffarelli, Luis A.; Friedman, Avner The blow-up boundary for nonlinear wave equations. Trans. Amer. Math. Soc. 297 (1986), no. 1, 223--241.

[81] Aguilera, N.; Alt, H. W.; Caffarelli, L. A. An optimization problem with volume constraint. SIAM J. Control Optim. 24 (1986), no. 2, 191--198.

[80] Caffarelli, Luis A.; Friedman, Avner Regularity of the boundary of a capillary drop on an inhomogeneous plane and related variational problems. Rev. Mat. Iberoamericana 1 (1985), no. 1, 61--84.

[79] Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner Abrupt and smooth separation of free boundaries in flow problems. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 12 (1985), no. 1, 137--172.

[78] Caffarelli, Luis A.; Friedman, Avner Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations. J. Differential Equations 60 (1985), no. 3, 420--433.

[77] Caffarelli, L.; Nirenberg, L.; Spruck, J. The Dirichlet problem for nonlinear second-order elliptic equations. III. Functions of the eigenvalues of the Hessian. Acta Math. 155 (1985), no. 3-4, 261--301.

[76] Athanasopoulos, Ioannis; Caffarelli, Luis A. A theorem of real analysis and its application to free boundary problems. Comm. Pure Appl. Math. 38 (1985), no. 5, 499--502,

[75] Caffarelli, Luis A.; Friedman, Avner Differentiability of the blow-up curve for one-dimensional nonlinear wave equations. Arch. Rational Mech. Anal. 91 (1985), no. 1, 83--98.

[74] Caffarelli, Luis A.; Friedman, Avner A nonlinear evolution problem associated with an electropaint process. SIAM J. Math. Anal. 16 (1985), no. 5, 955--969.

[73] Aronson, D. G.; Caffarelli, L. A.; Vázquez, Juan Luis Interfaces with a corner point in one-dimensional porous medium flow. Comm. Pure Appl. Math. 38 (1985), no. 4, 375--404.

[72] Caffarelli, Luis A.; Friedman, Avner Convexity of solutions of semilinear elliptic equations. Duke Math. J. 52 (1985), no. 2, 431--456.

[71] Caffarelli, L.; Kohn, J. J.; Nirenberg, L.; Spruck, J. The Dirichlet problem for nonlinear second-order elliptic equations. II. Complex Monge-Ampère, and uniformly elliptic, equations. Comm. Pure Appl. Math. 38 (1985), no. 2, 209--252.

[70] Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner Compressible flows of jets and cavities. J. Differential Equations 56 (1985), no. 1, 82--141.

[69] Caffarelli, Luis A. Variational problems with free boundaries. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), 1161--1163, PWN, Warsaw, 1984.

[68] Caffarelli, L.; Kohn, R.; Nirenberg, L. First order interpolation inequalities with weights. Compositio Math. 53 (1984), no. 3, 259--275.

[67] Caffarelli, Luis; Hardt, Robert; Simon, Leon Minimal surfaces with isolated singularities. Manuscripta Math. 48 (1984), no. 1-3, 1--18

[66] Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner The dam problem with two fluids. Comm. Pure Appl. Math. 37 (1984), no. 5, 601--645.

[65] Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner A free boundary problem for quasilinear elliptic equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 11 (1984), no. 1, 1--44.

[64] Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner Jets with two fluids. II. Two free boundaries. Indiana Univ. Math. J. 33 (1984), no. 3, 367--391.

[63] Caffarelli, L.; Nirenberg, L.; Spruck, J. The Dirichlet problem for nonlinear second-order elliptic equations. I. Monge-Ampère equation. Comm. Pure Appl. Math. 37 (1984), no. 3, 369--402.

[62] Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner Jets with two fluids. I. One free boundary. Indiana Univ. Math. J. 33 (1984), no. 2, 213--247.

[61] Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner Variational problems with two phases and their free boundaries. Trans. Amer. Math. Soc. 282 (1984), no. 2, 431--461.

[60] Aronson, D. G.; Caffarelli, L. A.; Kamin, S. How an initially stationary interface begins to move in porous medium flow. SIAM J. Math. Anal. 14 (1983), no. 4, 639--658.

[59] Caffarelli, L. A.; Evans, L. C. Continuity of the temperature in the two-phase Stefan problem. Arch. Rational Mech. Anal. 81 (1983), no. 3, 199--220.

[58] Alt, H. W.; Caffarelli, L. A.; Friedman, A. Axially symmetric jet flows. Arch. Rational Mech. Anal. 81 (1983), no. 2, 97--149.

[57] Caffarelli, L. A.; Evans, L. C. Continuity of the temperature in two-phase Stefan problems. Free boundary problems: theory and applications, Vol. I,II (Montecatini, 1981), 380--382, Res. Notes in Math. 78 Pitman, Boston, MA, 1983.

[56] Brezzi, F.; Caffarelli, L. A. Convergence of the discrete free boundaries for finite element approximations. RAIRO Anal. Numér. 17 (1983), no. 4, 385--395.

[55] Aronson, D. G.; Caffarelli, L. A. The initial trace of a solution of the porous medium equation. Trans. Amer. Math. Soc. 280 (1983), no. 1, 351--366.

[54] Caffarelli, L.; Kohn, R.; Nirenberg, L. Partial regularity of suitable weak solutions of the Navier-Stokes equations. Comm. Pure Appl. Math. 35 (1982), no. 6, 771--831.

[53] Caffarelli, Luis A.; Littman, Walter Representation formulas for solutions to $\Delta u-u=0$ in ${\bf R}^{n}$. Studies in partial differential equations 249--263, MAA Stud. Math. 23 Math. Assoc. America, Washington, DC, 1982.

[52] Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner Jet flows with gravity. J. Reine Angew. Math. 331 (1982), 58--103.

[51] Caffarelli, Luis A.; Friedman, Avner; Torelli, Alessandro The two-obstacle problem for the biharmonic operator. Pacific J. Math. 103 (1982), no. 2, 325--335.

[50] Caffarelli, L. A. Regularity theorems for weak solutions of some nonlinear systems. Comm. Pure Appl. Math. 35 (1982), no. 6, 833--838.

[49] Caffarelli, L.; Gidas, B.; Spruck, J. On multimeron solutions of the Yang-Mills equations. Comm. Math. Phys. 87 (1982/83), no. 4, 485--495.

[48] Caffarelli, Luis A.; Spruck, Joel Convexity properties of solutions to some classical variational problems. Comm. Partial Differential Equations 7 (1982), no. 11, 1337--1379.

[47] Caffarelli, Luis A.; Friedman, Avner Axially symmetric infinite cavities. Indiana Univ. Math. J. 31 (1982), no. 1, 135--160.

[46] Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner Asymmetric jet flows. Comm. Pure Appl. Math. 35 (1982), no. 1, 29--68.

[45] Caffarelli, Luis A.; Friedman, Avner Unloading in the elastic-plastic torsion problem. J. Differential Equations 41 (1981), no. 2, 186--217.

[44] Caffarelli, Luis A.; Friedman, Avner Sequential testing of several simple hypotheses for a diffusion process and the corresponding free boundary problem. Pacific J. Math. 93 (1981), no. 1, 49--94.

[43] Caffarelli, L.; Fabes, E.; Mortola, S.; Salsa, S. Boundary behavior of nonnegative solutions of elliptic operators in divergence form. Indiana Univ. Math. J. 30 (1981), no. 4, 621--640.

[42] Caffarelli, Luis A.; Fabes, Eugene B.; Kenig, Carlos E. Completely singular elliptic-harmonic measures. Indiana Univ. Math. J. 30 (1981), no. 6, 917--924.

[41] Alt, H. W.; Caffarelli, L. A. Existence and regularity for a minimum problem with free boundary. J. Reine Angew. Math. 325 (1981), 105--144.

[40] Caffarelli, Luis A.; Friedman, Avner; Visintin, Augusto A free boundary problem describing transition in a superconductor. SIAM J. Math. Anal. 12 (1981), no. 5, 679--690.

[39] Caffarelli, Luis A.; Friedman, Avner; Torelli, Alessandro The free boundary for a fourth order variational inequality. Illinois J. Math. 25 (1981), no. 3, 402--422.

[38] Caffarelli, Luis A. A remark on the Hausdorff measure of a free boundary, and the convergence of coincidence sets. Boll. Un. Mat. Ital. A (5) 18 (1981), no. 1, 109--113.

[37] Caffarelli, Luis A.; Friedman, Avner; Pozzi, Gianni Reflection methods in the elastic-plastic torsion problem. Indiana Univ. Math. J. 29 (1980), no. 2, 205--228.

[36] Caffarelli, Luis A.; Gilardi, Gianni Monotonicity of the free boundary in the two-dimensional dam problem. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 7 (1980), no. 3, 523--537.

[35] Caffarelli, Luis A.; Friedman, Avner Asymptotic estimates for the plasma problem. Duke Math. J. 47 (1980), no. 3, 705--742.

[34] Caffarelli, L. A.; Kinderlehrer, D. Potential methods in variational inequalities. J. Analyse Math. 37 (1980), 285--295.

[33] Caffarelli, Luis A.; Friedman, Avner Regularity of the free boundary of a gas flow in an $n$-dimensional porous medium. Indiana Univ. Math. J. 29 (1980), no. 3, 361--391.

[32] Caffarelli, Luis A.; Friedman, Avner A free boundary problem associated with a semilinear parabolic equation. Comm. Partial Differential Equations 5 (1980), no. 9, 969--981.

[31] Brèzis, Haïm; Caffarelli, Luis A.; Friedman, Avner Reinforcement problems for elliptic equations and variational inequalities. Ann. Mat. Pura Appl. (4) 123 (1980), 219--246.

[30] Caffarelli, Luis A.; Friedman, Avner Reinforcement problems in elastoplasticity. Rocky Mountain J. Math. 10 (1980), no. 1, 155--184.

[29] Caffarelli, Luis A.; Friedman, Avner The shape of axisymmetric rotating fluid. J. Funct. Anal. 35 (1980), no. 1, 109--142.

[28] Caffarelli, Luis A. Compactness methods in free boundary problems. Comm. Partial Differential Equations 5 (1980), no. 4, 427--448.

[27] Caffarelli, Luis A.; Friedman, Avner Regularity of the solution of the quasivariational inequality for the impulse control problem. II. Comm. Partial Differential Equations 4 (1979), no. 3, 279--291.

[26] Caffarelli, Luis A.; Friedman, Avner Regularity of the free boundary for the one-dimensional flow of gas in a porous medium. Amer. J. Math. 101 (1979), no. 6, 1193--1218.

[25] Caffarelli, L. A. Further regularity for the Signorini problem. Comm. Partial Differential Equations 4 (1979), no. 9, 1067--1075.

[24] Caffarelli, Luis A.; Friedman, Avner Continuity of the density of a gas flow in a porous medium. Trans. Amer. Math. Soc. 252 (1979), 99--113.

[23] Caffarelli, Luis A.; Friedman, Avner The free boundary for elastic-plastic torsion problems. Trans. Amer. Math. Soc. 252 (1979), 65--97.

[22] Caffarelli, Luis A.; Friedman, Avner Continuity of the temperature in the Stefan problem. Indiana Univ. Math. J. 28 (1979), no. 1, 53--70.

[21] Caffarelli, Luis A.; Friedman, Avner The free boundary in the Thomas-Fermi atomic model. J. Differential Equations 32 (1979), no. 3, 335--356.

[20] Caffarelli, Luis A.; Friedman, Avner The obstacle problem for the biharmonic operator. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 6 (1979), no. 1, 151--184.

[19] Caffarelli, L. A.; Rivière, N. M. The Lipschitz character of the stress tensor, when twisting an elastic plastic bar. Arch. Rational Mech. Anal. 69 (1979), no. 1, 31--36.

[18] Caffarelli, Luis A. The continuity of the temperature in the Stefan problem. Proceedings of the International Meeting on Recent Methods in Nonlinear Analysis (Rome, 1978), pp. 13--23, Pitagora, Bologna, 1979

[17] Caffarelli, Luis A.; Friedman, Avner Asymptotic estimates for the dam problem with several layers. Indiana Univ. Math. J. 27 (1978), no. 4, 551--580.

[16] Caffarelli, Luis A.; Friedman, Avner The one-phase Stefan problem and the porous medium diffusion equation: continuity of the solution in $n$ space dimensions. Proc. Nat. Acad. Sci. U.S.A. 75 (1978), no. 5, 2084.

[15] Caffarelli, Luis A.; Friedman, Avner The dam problem with two layers. Arch. Rational Mech. Anal. 68 (1978), no. 2, 125--154.

[14] Caffarelli, Luis A.; Friedman, Avner Regularity of the solution of the quasivariational inequality for the impulse control problem. Comm. Partial Differential Equations 3 (1978), no. 8, 745--753.

[13] Caffarelli, Luis A. Some aspects of the one-phase Stefan problem. Indiana Univ. Math. J. 27 (1978), no. 1, 73--77.

[12] Caffarelli, L. A.; Rivière, Nèstor M. The smoothness of the elastic-plastic free boundary of a twisted bar. Proc. Amer. Math. Soc. 63 (1977), no. 1, 56--58.

[11] Caffarelli, L. A.; Rivière, Nèstor M. Asymptotic behaviour of free boundaries at their singular points. Ann. Math. (2) 106 (1977), no. 2, 309--317.

[10] Caffarelli, Luis A. The regularity of free boundaries in higher dimensions. Acta Math. 139 (1977), no. 3-4, 155--184.

[9] Caffarelli, Luis A. The smoothness of the free surface in a filtration problem. Arch. Rational Mech. Anal. 63 (1976), no. 1, 77--86.

[8] Caffarelli, L. A.; Rivière, N. M. Smoothness and analyticity of free boundaries in variational inequalities. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1976), no. 2, 289--310.

[7] Caffarelli, L. A.; Rivière, N. M. On the rectifiability of domains with finite perimeter. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1976), no. 2, 177--186.

[6] Caffarelli, Luis A. The regularity of elliptic and parabolic free boundaries. Bull. Amer. Math. Soc. 82 (1976), no. 4, 616--618.

[5] Caffarelli, Luis A. On the Hölder continuity of multiple valued harmonic functions. Indiana Univ. Math. J. 25 (1976), no. 1, 79--84.

[4] Caffarelli, L. A. Certain multiple valued harmonic function. Proc. Amer. Math. Soc. 54 (1976), 90--92.

[3] Caffarelli, Luis A. Surfaces of minimum capacity for a knot. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 2 (1975), no. 4, 497--505.

[2] Caffarelli, Luis A.; Calderón, Calixto P. On Abel summability of multiple Jacobi series. Colloq. Math. 30 (1974), 277--288.

[1] Caffarelli, Luis A.; Calderón, Calixto P. Weak type estimates for the Hardy-Littlewood maximal functions. Studia Math. 49 (1973/74), 217--223.