Edit Profile (opens in new tab) Caffarelli, Luis Ángel Co-Author Distance Author ID: caffarelli.luis-a Published as: Caffarelli, Luis A.; Caffarelli, Luis; Caffarelli, L. A.; Caffarelli, L.; Caffarelli, Luis Ángel; Cafferelli, L. A. more...less Homepage: https://web.ma.utexas.edu/users/caffarel/ External Links: MGP · ORCID · Wikidata · Google Scholar · Math-Net.Ru · dblp · GND · IdRef Awards: Wolf Prize (2012) · Shaw Prize (2018) · Abel Prize (2023) Documents Indexed: 312 Publications since 1974, including 4 Books and 3 Additional arXiv Preprints 7 Contributions as Editor · 3 Further Contributions Biographic References: 4 Publications Co-Authors: 132 Co-Authors with 262 Joint Publications 4,017 Co-Co-Authors all top 5 Co-Authors 58 single-authored 43 Friedman, Avner 18 Nirenberg, Louis 13 Athanasopoulos, Ioannis 13 Spruck, Joel 12 Alt, Hans Wilhelm 11 Salsa, Sandro 10 Silvestre, Luis E. 9 Mellet, Antoine 8 Vazquez, Juan Luis 7 Li, YanYan 7 Roquejoffre, Jean-Michel 6 Berestycki, Henri 6 Lin, Fang Hua 6 Markowich, Peter Alexander 6 Sire, Yannick 6 Vasseur, Alexis F. 5 Kenig, Carlos Eduardo 5 Lee, Ki-Ahm 5 Riviere, Nestor M. 5 Savin, Ovidiu V. 5 Shahgholian, Henrik 5 Valdinoci, Enrico 4 Arapostathis, Aristotle 4 Aronson, Donald G. 4 Cabré, Xavier 4 Córdoba Barba, Antonio Juan 4 Crandall, Michael G. 4 Figalli, Alessio 4 Gutiérrez, Cristian E. 4 Souganidis, Panagiotis E. 4 Wang, Lihe 4 Wolanski, Noemi I. 3 Aguilera, Néstor E. 3 Ambrosio, Luigi 3 Biswas, Anup 3 Burger, Martin 3 De Silva, Daniela 3 Huang, Qingbo 3 Jerison, David S. 3 Kohn, Robert Vita 3 Milakis, Emmanouil 3 Stinga, Pablo Raúl 3 Wolfram, Marie-Therese 2 Allen, Mark G. 2 Bjorland, Clayton 2 Bonforte, Matteo 2 Brézis, Haïm 2 Calderón, Calixto Pedro 2 de la Llave, Rafael 2 Dundas, Bjørn Ian 2 Evans, Lawrence Craig 2 Fabes, Eugene B. 2 Gidas, Basilis 2 Grillo, Gabriele 2 Karakhanyan, Aram L. 2 Kinderlehrer, David 2 Kohn, Joseph J. 2 Lederman, Claudia B. 2 McCann, Robert J. 2 Milman, Mario Marcos 2 Oliker, Vladimir I. 2 Patrizi, Stefania 2 Quitalo, Veronica 2 Salazar, Jorge A. 2 Skau, Christian Fredrik 2 Soria-Carro, María 2 Tomasetti, Ignacio 2 Torelli, Alessandro 2 Urbano, José Miguel 2 Vivas, Hernán Agustín 2 Yuan, Yu 1 Agmon, Shmuel 1 Birindelli, Isabeau 1 Brenier, Yann 1 Brezzi, Franco 1 Buttazzo, Giuseppe 1 Cagnetti, Filippo 1 Chan, Chi Hin 1 Chang, Kung-Ching 1 Chang, Sun-Yung Alice 1 Charro, Fernando 1 Dávila, Gonzalo 1 Guedes de Figueiredo, Djairo 1 Dipierro, Serena 1 Dolbeault, Jean 1 Duque, Luis 1 E, Weinan 1 Ekeland, Ivar 1 Fefferman, Charles Louis 1 Feldman, Mikhail 1 Garofalo, Nicola 1 Gilardi, Gianni 1 Glowinski, Roland 1 González, María del Mar 1 Gualdani, Maria Pia 1 Guan, Pengfei 1 Hardt, Robert M. 1 Jin, Tianling 1 Kamin, Shoshana 1 Karp, Lavi ...and 50 more Co-Authors all top 5 Serials 36 Communications on Pure and Applied Mathematics 23 Archive for Rational Mechanics and Analysis 21 Indiana University Mathematics Journal 18 Communications in Partial Differential Equations 12 Annals of Mathematics. Second Series 10 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 8 Transactions of the American Mathematical Society 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 6 Advances in Mathematics 5 Duke Mathematical Journal 5 Journal of Differential Equations 5 Journal für die Reine und Angewandte Mathematik 5 Proceedings of the American Mathematical Society 5 Journal of the American Mathematical Society 5 Discrete and Continuous Dynamical Systems 4 American Journal of Mathematics 4 Calculus of Variations and Partial Differential Equations 3 Communications in Mathematical Physics 3 Acta Mathematica 3 Inventiones Mathematicae 3 Revista Matemática Iberoamericana 3 Differential and Integral Equations 3 SIAM Journal on Mathematical Analysis 3 Journal of the European Mathematical Society (JEMS) 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Pacific Journal of Mathematics 2 SIAM Journal on Control and Optimization 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Notices of the American Mathematical Society 2 Communications in Analysis and Geometry 2 Journal of Mathematical Sciences (New York) 2 St. Petersburg Mathematical Journal 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Fixed Point Theory and Applications 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Rocky Mountain Journal of Mathematics 1 Studia Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Calcolo 1 Colloquium Mathematicum 1 Compositio Mathematica 1 Illinois Journal of Mathematics 1 Journal of Functional Analysis 1 Manuscripta Mathematica 1 Mathematische Annalen 1 RAIRO. Analyse Numérique 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Chinese Annals of Mathematics. Series B 1 Journal of Scientific Computing 1 The Journal of Geometric Analysis 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the National Academy of Sciences of the United States of America 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 Bollettino della Unione Matemàtica Italiana. Serie VII. B 1 Journal of Partial Differential Equations 1 Journal of Dynamics and Differential Equations 1 Topological Methods in Nonlinear Analysis 1 The Journal of Fourier Analysis and Applications 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Interfaces and Free Boundaries 1 Journal of Numerical Mathematics 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Communications in Mathematical Sciences 1 Analysis in Theory and Applications 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Bollettino della Unione Matematica Italiana. Series V. A 1 Bulletin of the American Mathematical Society 1 Colloquium Publications. American Mathematical Society 1 Contemporary Mathematics 1 Graduate Studies in Mathematics 1 Lecture Notes in Mathematics 1 IAS/Park City Mathematics Series 1 Networks and Heterogeneous Media 1 Discrete and Continuous Dynamical Systems. Series S 1 Kinetic and Related Models 1 Analysis & PDE 1 Annals of PDE 1 Philosophical Transactions A. Royal Society of London 1 Mathematics in Engineering 1 European Mathematical Society Magazine all top 5 Fields 266 Partial differential equations (35-XX) 69 Calculus of variations and optimal control; optimization (49-XX) 42 Fluid mechanics (76-XX) 17 Differential geometry (53-XX) 16 Potential theory (31-XX) 12 Global analysis, analysis on manifolds (58-XX) 12 Mechanics of deformable solids (74-XX) 11 Operator theory (47-XX) 11 Classical thermodynamics, heat transfer (80-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 General and overarching topics; collections (00-XX) 8 Integral equations (45-XX) 8 Optics, electromagnetic theory (78-XX) 7 History and biography (01-XX) 7 Real functions (26-XX) 7 Functional analysis (46-XX) 7 Probability theory and stochastic processes (60-XX) 7 Numerical analysis (65-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Statistical mechanics, structure of matter (82-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Systems theory; control (93-XX) 3 Measure and integration (28-XX) 3 Quantum theory (81-XX) 2 Ordinary differential equations (34-XX) 2 Convex and discrete geometry (52-XX) 2 Operations research, mathematical programming (90-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 290 Publications have been cited 19,120 times in 10,989 Documents Cited by ▼ Year ▼ An extension problem related to the fractional Laplacian. Zbl 1143.26002 Caffarelli, Luis; Silvestre, Luis 1,809 2007 Fully nonlinear elliptic equations. Zbl 0834.35002 Caffarelli, Luis A.; Cabré, Xavier 824 1995 Partial regularity of suitable weak solutions of the Navier-Stokes equations. Zbl 0509.35067 Caffarelli, L.; Kohn, R.; Nirenberg, Louis 737 1982 Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Zbl 0702.35085 Caffarelli, Luis A.; Gidas, Basilis; Spruck, Joel 680 1989 First order interpolation inequalities with weights. Zbl 0563.46024 Caffarelli, L.; Kohn, R.; Nirenberg, Louis 628 1984 Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Zbl 1204.35063 Caffarelli, Luis A.; Vasseur, Alexis 532 2010 The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian. Zbl 0654.35031 Caffarelli, L.; Nirenberg, L.; Spruck, J. 467 1985 Existence and regularity for a minimum problem with free boundary. Zbl 0449.35105 Alt, H. W.; Caffarelli, L. A. 410 1981 Regularity theory for fully nonlinear integro-differential equations. Zbl 1170.45006 Caffarelli, Luis; Silvestre, Luis 359 2009 Interior a priori estimates for solutions of fully nonlinear equations. Zbl 0692.35017 Caffarelli, Luis A. 353 1989 On \(W^{1,p}\) estimates for elliptic equations in divergence form. Zbl 0906.35030 Caffarelli, L. A.; Peral, I. 327 1998 Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Zbl 1148.35097 Caffarelli, Luis A.; Salsa, Sandro; Silvestre, Luis 325 2008 The Dirichlet problem for nonlinear second-order elliptic equations. I: Monge-Ampère equation. Zbl 0598.35047 Caffarelli, L.; Nirenberg, Louis; Spruck, J. 321 1984 Non-local diffusions, drifts and games. Zbl 1266.35060 Caffarelli, Luis 275 2012 Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation. Zbl 0704.35044 Caffarelli, Luis A. 269 1990 Nonlocal minimal surfaces. Zbl 1248.53009 Caffarelli, L.; Roquejoffre, J.-M.; Savin, O. 260 2010 Variational problems with two phases and their free boundary. Zbl 0844.35137 Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 241 1984 The obstacle problem revisited. Zbl 0928.49030 Caffarelli, L. A. 226 1998 A geometric approach to free boundary problems. Zbl 1083.35001 Caffarelli, Luis; Salsa, Sandro 219 2005 The regularity of free boundaries in higher dimensions. Zbl 0386.35046 Caffarelli, Luis A. 191 1978 On viscosity solutions of fully nonlinear equations with measurable ingredients. Zbl 0854.35032 Caffarelli, L.; Crandall, M. G.; Kocan, M.; Świȩch, A. 191 1996 Variational problems with free boundaries for the fractional Laplacian. Zbl 1221.35453 Caffarelli, Luis A.; Roquejoffre, Jean-Michel; Sire, Yannick 174 2010 Boundary behavior of nonnegative solutions of elliptic operators in divergence form. Zbl 0512.35038 Caffarelli, L.; Fabes, E.; Mortola, S.; Salsa, S. 174 1981 A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity. Zbl 0704.35045 Caffarelli, L. A. 170 1990 Monotonicity for elliptic equations in unbounded Lipschitz domains. Zbl 0906.35035 Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 162 1997 Further qualitative properties for elliptic equations in unbounded domains. Zbl 1079.35513 Berestycki, Henri; Caffarelli, Luis; Nirenberg, Louis 162 1997 The Dirichlet problem for nonlinear second-order elliptic equations. II: Complex Monge-Ampère, and uniformly elliptic, equations. Zbl 0598.35048 Caffarelli, L.; Kohn, J. J.; Nirenberg, Louis; Spruck, J. 158 1985 The regularity of mappings with a convex potential. Zbl 0753.35031 Caffarelli, Luis A. 152 1992 Regularity results for nonlocal equations by approximation. Zbl 1231.35284 Caffarelli, Luis; Silvestre, Luis 144 2011 Vortex condensation in the Chern-Simons Higgs model: An existence theorem. Zbl 0846.58063 Caffarelli, Luis A.; Yang, Yisong 140 1995 Fractional elliptic equations, Caccioppoli estimates and regularity. Zbl 1381.35211 Caffarelli, Luis A.; Stinga, Pablo Raúl 139 2016 A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are \(C^{1,\alpha}\). Zbl 0676.35085 Caffarelli, Luis A. 136 1987 A Harnack inequality approach to the regularity of free boundaries. II: Flat free boundaries are Lipschitz. Zbl 0676.35086 Caffarelli, Luis A. 131 1989 Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105 Caffarelli, Luis; Vazquez, Juan Luis 130 2011 Some regularity properties of solutions of Monge Ampère equation. Zbl 0761.35028 Caffarelli, Luis A. 122 1991 A parabolic problem with a fractional time derivative. Zbl 1338.35428 Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 120 2016 Convexity of solutions of semilinear elliptic equations. Zbl 0599.35065 Caffarelli, Luis A.; Friedman, Avner 117 1985 Uniform estimates and limiting arguments for nonlocal minimal surfaces. Zbl 1357.49143 Caffarelli, Luis; Valdinoci, Enrico 110 2011 Boundary regularity of maps with convex potentials. II. Zbl 0916.35016 Caffarelli, Luis A. 106 1996 Regularity theory for parabolic nonlinear integral operators. Zbl 1223.35098 Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis 103 2011 Convexity properties of solutions to some classical variational problems. Zbl 0508.49013 Caffarelli, Luis A.; Spruck, Joel 102 1982 Inequalities for second-order elliptic equations with applications to unbounded domains. I. Zbl 0860.35004 Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 95 1996 The initial trace of a solution of the porous medium equation. Zbl 0556.76084 Aronson, D. G.; Caffarelli, L. A. 93 1983 Properties of the solutions of the linearized Monge-Ampère equation. Zbl 0878.35039 Caffarelli, Luis A.; Gutiérrez, Cristian E. 90 1997 Monotonicity properties of optimal transportation and the FKG and related inequalities. Zbl 0978.60107 Caffarelli, Luis A. 89 2000 An extension to a theorem of Jörgens, Calabi, and Pogorelov. Zbl 1236.35041 Caffarelli, L.; Li, YanYan 88 2003 A Harnack inequality approach to the regularity of free boundaries. III: Existence theory, compactness, and dependence on X. Zbl 0702.35249 Caffarelli, Luis A. 87 1988 The Evans-Krylov theorem for nonlocal fully nonlinear equations. Zbl 1232.49043 Caffarelli, Luis; Silvestre, Luis 87 2011 Nonlinear second-order elliptic equations. V: The Dirichlet problem for Weingarten hypersurfaces. Zbl 0672.35028 Caffarelli, Luis; Nirenberg, Louis; Spruck, Joel 86 1988 Regularity of the free boundary of a gas flow in an \(n\)-dimensional porous medium. Zbl 0439.76085 Caffarelli, Luis A.; Friedman, Avner 84 1980 Boundary regularity of maps with convex potentials. Zbl 0778.35015 Caffarelli, Luis A. 83 1992 Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. Zbl 1194.35138 Caffarelli, L. A.; Lin, Fang-Hua 82 2008 An \(L^ \infty\) bound for solutions of the Cahn-Hilliard equation. Zbl 0851.35010 Caffarelli, Luis A.; Muler, Nora E. 81 1995 The structure of the free boundary for lower dimensional obstacle problems. Zbl 1185.35339 Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S. 79 2008 Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs. Zbl 1053.49032 Caffarelli, Luis A.; Feldman, Mikhail; McCann, Robert J. 79 2002 Uniform estimates for regularization of free boundary problems. Zbl 0702.35252 Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 75 1990 Further regularity for the Signorini problem. Zbl 0427.35019 Caffarelli, L. A. 75 1979 Regularity of a free boundary with application to the Pompeiu problem. Zbl 0960.35112 Caffarelli, Luis A.; Karp, Lavi; Shahgholian, Henrik 75 2000 Global energy minimizers for free boundary problems and full regularity in three dimensions. Zbl 1330.35545 Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E. 75 2004 A free boundary problem for quasi-linear elliptic equations. Zbl 0554.35129 Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 72 1984 Continuity of the temperature in the two-phase Stefan problem. Zbl 0516.35080 Caffarelli, L. A.; Evans, L. C. 72 1983 Lipschitz continuity of solutions and interfaces of the N-dimensional porous medium equation. Zbl 0644.35058 Caffarelli, L. A.; Vazquez, J. L.; Wolanski, N. I. 70 1987 Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media. Zbl 1063.35025 Caffarelli, Luis A.; Souganidis, Panagiotis E.; Wang, L. 70 2005 Some new monotonicity theorems with applications to free boundary problems. Zbl 1142.35382 Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E. 70 2002 Non-local gradient dependent operators. Zbl 1252.35099 Bjorland, C.; Caffarelli, L.; Figalli, A. 68 2012 Nonlinear second order elliptic equations. IV. Starshaped compact Weingarten hypersurfaces. Zbl 0672.35027 Caffarelli, L.; Nirenberg, L.; Spruck, J. 67 1986 Optimal regularity of lower dimensional obstacle problems. Zbl 1108.35038 Athanasopoulos, I.; Caffarelli, L. A. 67 2004 An optimal partition problem for eigenvalues. Zbl 1123.65060 Cafferelli, L. A.; Lin, Fang Hua 66 2007 Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088 Caffarelli, Luis; Figalli, Alessio 65 2013 Completely singular elliptic-harmonic measures. Zbl 0482.35020 Caffarelli, Luis A.; Fabes, Eugene B.; Kenig, Carlos E. 65 1981 Free boundaries in optimal transport and Monge-Ampère obstacle problems. Zbl 1196.35231 Caffarelli, Luis A.; McCann, Robert J. 64 2010 Optimal transportation and applications. Lectures given at the C. I. M. E. summer school, Martina Franca, Italy, September 2–8, 2001. Zbl 1013.00028 Ambrosio, Luigi; Brenier, Yann; Buttazzo, Giusseppe; Caffarelli, Luis A.; Villani, Cédric 64 2003 Uniform convergence of a singular perturbation problem. Zbl 0829.49013 Caffarelli, Luis A.; Córdoba, Antonio 64 1995 The obstacle problem for the biharmonic operator. Zbl 0405.31007 Caffarelli, Luis A.; Friedman, Avner 63 1979 A free-boundary problem for the heat equation arising in flame propagation. Zbl 0814.35149 Caffarelli, Luis A.; Vázquez, Juan L. 63 1995 Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312 Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis 62 2013 Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations. Zbl 0593.35047 Caffarelli, Luis A.; Friedman, Avner 62 1985 Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278 Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio 61 2012 Regularity properties of nonlocal minimal surfaces via limiting arguments. Zbl 1284.53008 Caffarelli, Luis; Valdinoci, Enrico 59 2013 Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043 Caffarelli, Luis; Vázquez, Juan-Luis 57 2011 Compactness methods in free boundary problems. Zbl 0437.35070 Caffarelli, Luis A. 56 1980 A gradient bound for entire solutions of quasi-linear equations and its consequences. Zbl 0819.35016 Caffarelli, Luis; Garofalo, Nicola; Segala, Fausto 56 1994 Continuity of the density of a gas flow in a porous medium. Zbl 0425.35060 Caffarelli, Luis A.; Friedman, Avner 54 1979 Rates of convergence for the homogenization of fully nonlinear uniformly elliptic PDE in random media. Zbl 1192.35048 Caffarelli, Luis A.; Souganidis, Panagiotis E. 53 2010 Potential methods in variational inequalities. Zbl 0455.49010 Caffarelli, L. A.; Kinderlehrer, D. 51 1980 Regularity of a free boundary in parabolic potential theory. Zbl 1054.35142 Caffarelli, Luis; Petrosyan, Arshak; Shahgholian, Henrik 51 2004 Axially symmetric jet flows. Zbl 0515.76017 Alt, H. W.; Caffarelli, L. A.; Friedman, A. 51 1983 The blow-up boundary for nonlinear wave equations. Zbl 0638.35053 Caffarelli, Luis A.; Friedman, Avner 49 1986 On the case of equality in the Brunn-Minkowski inequality for capacity. Zbl 0847.31005 Caffarelli, Luis A.; Jerison, David; Lieb, Elliott H. 49 1996 An optimization problem with volume constraint. Zbl 0588.49005 Aguilera, N.; Alt, H. W.; Caffarelli, L. A. 48 1986 Convergence of nonlocal threshold dynamics approximations to front propagation. Zbl 1190.65132 Caffarelli, Luis A.; Souganidis, Panagiotis E. 48 2010 Some remarks on singular solutions of nonlinear elliptic equations. III: Viscosity solutions including parabolic operators. Zbl 1279.35044 Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis 47 2013 Obstacle problems for integro-differential operators: regularity of solutions and free boundaries. Zbl 1371.35361 Caffarelli, Luis; Ros-Oton, Xavier; Serra, Joaquim 47 2017 Planelike minimizers in periodic media. Zbl 1036.49040 Caffarelli, Luis A.; de la Llave, Rafael 47 2001 Real analysis related to the Monge-Ampère equation. Zbl 0858.35034 Caffarelli, Luis A.; Gutiérrez, Cristian E. 47 1996 How an initially stationary interface begins to move in porous medium flow. Zbl 0542.76119 Aronson, D. G.; Caffarelli, L. A.; Kamin, S. 46 1983 The shape of axisymmetric rotating fluid. Zbl 0439.35068 Caffarelli, Luis A.; Friedman, Avner 46 1980 Symmetry for elliptic equations in a half space. Zbl 0793.35034 Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 46 1993 Asymptotic estimates for the plasma problem. Zbl 0466.35033 Caffarelli, Luis A.; Friedman, Avner 46 1980 Continuity of the temperature in boundary heat control problems. Zbl 1190.35125 Athanasopoulos, I.; Caffarelli, L. A. 45 2010 On a family of fully nonlinear integrodifferential operators: from fractional Laplacian to nonlocal Monge-Ampère. Zbl 1533.35130 Caffarelli, Luis A.; Soria-Carro, María 2 2024 Fully nonlinear equations with applications to Grad equations in plasma physics. Zbl 1532.35123 Caffarelli, Luis A.; Tomasetti, Ignacio 1 2023 The two-phase Stefan problem with anomalous diffusion. Zbl 1495.35176 Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil 2 2022 Singular solutions to Monge-Ampère equation. Zbl 1513.35274 Caffarelli, Luis A.; Yuan, Yu 1 2022 Global \(C^{1,\alpha}\) regularity for Monge-Ampère equation and convex envelope. Zbl 1496.35223 Caffarelli, Luis A.; Tang, Lan; Wang, Xu-Jia 1 2022 Regularity for \(C^{1, \alpha}\) interface transmission problems. Zbl 1467.35169 Caffarelli, Luis Ángel; Soria-Carro, María; Stinga, Pablo Raúl 14 2021 The leading edge of a free boundary interacting with a line of fast diffusion. Zbl 1465.35414 Caffarelli, L. A.; Roquejoffre, J.-M. 1 2021 Fully nonlinear integro-differential equations with deforming kernels. Zbl 1452.35055 Caffarelli, Luis; Teymurazyan, Rafayel; Urbano, José Miguel 6 2020 Existence of weak solutions to a continuity equation with space time nonlocal Darcy law. Zbl 1459.35233 Caffarelli, Luis; Gualdani, Maria; Zamponi, Nicola 5 2020 Optimal regularity and structure of the free boundary for minimizers in cohesive zone models. Zbl 1442.49005 Caffarelli, L.; Cagnetti, F.; Figalli, A. 4 2020 Minimal surfaces and free boundaries: recent developments. Zbl 1433.35464 Caffarelli, Luis A.; Sire, Yannick 2 2020 Ergodic control of a class of jump diffusions with finite Lévy measures and rough kernels. Zbl 1415.93288 Arapostathis, Ari; Caffarelli, Luis; Pang, Guodong; Zheng, Yi 8 2019 Interior regularity for fractional systems. Zbl 1411.35111 Caffarelli, Luis; Dávila, Gonzalo 7 2019 Parabolic obstacle problems, quasi-convexity and regularity. Zbl 1432.35264 Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil 6 2019 On uniqueness of solutions to viscous HJB equations with a subquadratic nonlinearity in the gradient. Zbl 1428.35125 Arapostathis, Ari; Biswas, Anup; Caffarelli, Luis 5 2019 Regularity of interfaces for a Pucci type segregation problem. Zbl 1432.35085 Caffarelli, L.; Patrizi, S.; Quitalo, V.; Torres, M. 3 2019 On the regularity of the non-dynamic parabolic fractional obstacle problem. Zbl 1394.35588 Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil 25 2018 A minimization problem with free boundary related to a cooperative system. Zbl 1395.35226 Caffarelli, Luis A.; Shahgholian, Henrik; Yeressian, Karen 24 2018 Two-phase anisotropic free boundary problems and applications to the Bellman equation in 2D. Zbl 1393.35247 Caffarelli, L.; De Silva, D.; Savin, O. 7 2018 Bounds on the Green function for integral operators and fractional harmonic measure with applications to boundary Harnack. Zbl 1387.35071 Caffarelli, Luis A.; Sire, Yannick 3 2018 The two membranes problem for fully nonlinear operators. Zbl 1524.35780 Caffarelli, Luis; Duque, Luis; Vivas, Hernán 3 2018 Obstacle problems for integro-differential operators: regularity of solutions and free boundaries. Zbl 1371.35361 Caffarelli, Luis; Ros-Oton, Xavier; Serra, Joaquim 47 2017 Porous medium flow with both a fractional potential pressure and fractional time derivative. Zbl 1372.35328 Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 28 2017 A logistic equation with nonlocal interactions. Zbl 1356.35261 Caffarelli, Luis; Dipierro, Serena; Valdinoci, Enrico 28 2017 The two membranes problem for different operators. Zbl 1368.35045 Caffarelli, L.; De Silva, D.; Savin, O. 20 2017 On some pointwise inequalities involving nonlocal operators. Zbl 1482.35017 Caffarelli, Luis A.; Sire, Yannick 19 2017 On a long range segregation model. Zbl 1386.35084 Caffarelli, L.; Patrizi, S.; Quitalo, V. 9 2017 Fractional elliptic equations, Caccioppoli estimates and regularity. Zbl 1381.35211 Caffarelli, Luis A.; Stinga, Pablo Raúl 139 2016 A parabolic problem with a fractional time derivative. Zbl 1338.35428 Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 120 2016 A free boundary problem related to thermal insulation. Zbl 1351.35268 Caffarelli, Luis A.; Kriventsov, Dennis 21 2016 Regularity of solutions of the fractional porous medium flow with exponent \(1/2\). Zbl 1335.35273 Caffarelli, L.; Vázquez, J. L. 19 2016 The Dirichlet problem for stable-like operators and related probabilistic representations. Zbl 1352.60080 Arapostathis, Ari; Biswas, Anup; Caffarelli, Luis 17 2016 Obstacle-type problems for minimal surfaces. Zbl 1370.35070 Caffarelli, L.; De Silva, D.; Savin, O. 16 2016 A non-local Monge-Ampère equation. Zbl 1361.35067 Caffarelli, Luis; Silvestre, Luis 10 2016 Foreword: In honor of Juan Luis Vázquez for his 70th birthday. Zbl 1334.00104 1 2016 On a fractional Monge-Ampère operator. Zbl 1393.35268 Caffarelli, Luis; Charro, Fernando 18 2015 Minimization of a fractional perimeter-Dirichlet integral functional. Zbl 1323.35216 Caffarelli, Luis; Savin, Ovidiu; Valdinoci, Enrico 14 2015 Regularity of free boundaries a heuristic retro. Zbl 1353.35319 Caffarelli, Luis A.; Shahgholian, Henrik 4 2015 A bifurcation phenomenon in a singularly perturbed one-phase free boundary problem of phase transition. Zbl 1334.35439 Caffarelli, Luis A.; Wang, Peiyong 3 2015 Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities. Zbl 1296.35208 Caffarelli, Luis; Jin, Tianling; Sire, Yannick; Xiong, Jingang 41 2014 Partial differential equation models in the socio-economic sciences. Zbl 1353.00004 18 2014 Hölder regularity for generalized master equations with rough kernels. Zbl 1312.45013 Caffarelli, Luis; Silvestre, Luis 14 2014 Regularity for anisotropic fully nonlinear integro-differential equations. Zbl 1304.35730 Caffarelli, Luis A.; Leitão, Raimundo; Urbano, José Miguel 11 2014 Counter-example in three dimension and homogenization of geometric motions in two dimension. Zbl 1293.35026 Caffarelli, L. A.; Monneau, R. 9 2014 On the asymptotic behavior of a Boltzmann-type price formation model. Zbl 1307.35302 Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 8 2014 A perturbation argument for a Monge-Ampère type equation arising in optimal transportation. Zbl 1294.35170 Caffarelli, Luis; Del Mar González, María; Nguyen, Truyen 6 2014 Relations between geometric convexity, doubling measures and property \(\Gamma\). Zbl 1307.46006 Caffarelli, Luis A.; Crandall, Michael G. 2 2014 Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088 Caffarelli, Luis; Figalli, Alessio 65 2013 Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312 Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis 62 2013 Regularity properties of nonlocal minimal surfaces via limiting arguments. Zbl 1284.53008 Caffarelli, Luis; Valdinoci, Enrico 59 2013 Some remarks on singular solutions of nonlinear elliptic equations. III: Viscosity solutions including parabolic operators. Zbl 1279.35044 Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis 47 2013 On a Boltzmann-type price formation model. Zbl 1372.91039 Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 19 2013 A priori bounds for solutions of a nonlocal evolution PDE. Zbl 1273.35067 Caffarelli, Luis; Valdinoci, Enrico 9 2013 The homogenization of surfaces and boundaries. Zbl 1296.35030 Caffarelli, Luis 3 2013 Non-local diffusions, drifts and games. Zbl 1266.35060 Caffarelli, Luis 275 2012 Non-local gradient dependent operators. Zbl 1252.35099 Bjorland, C.; Caffarelli, L.; Figalli, A. 68 2012 Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278 Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio 61 2012 Some remarks on singular solutions of nonlinear elliptic equations. II: Symmetry and monotonicity via moving planes. Zbl 1325.35044 Caffarelli, Luis; Li, YanYan; Nirenberg, Louis 21 2012 Traveling waves for a boundary reaction-diffusion equation. Zbl 1255.35072 Caffarelli, L.; Mellet, A.; Sire, Y. 13 2012 The De Giorgi method for nonlocal fluid dynamics. Zbl 1357.35249 Caffarelli, Luis A.; Vasseur, Alexis 6 2012 The problem of two sticks. Zbl 1257.46009 Caffarelli, Luis A.; Crandall, Michael G. 1 2012 Regularity results for nonlocal equations by approximation. Zbl 1231.35284 Caffarelli, Luis; Silvestre, Luis 144 2011 Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105 Caffarelli, Luis; Vazquez, Juan Luis 130 2011 Uniform estimates and limiting arguments for nonlocal minimal surfaces. Zbl 1357.49143 Caffarelli, Luis; Valdinoci, Enrico 110 2011 Regularity theory for parabolic nonlinear integral operators. Zbl 1223.35098 Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis 103 2011 The Evans-Krylov theorem for nonlocal fully nonlinear equations. Zbl 1232.49043 Caffarelli, Luis; Silvestre, Luis 87 2011 Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043 Caffarelli, Luis; Vázquez, Juan-Luis 57 2011 On a price formation free boundary model by Lasry and Lions. Zbl 1216.91012 Caffarelli, Luis A.; Markowich, Peter A.; Pietschmann, Jan-F. 15 2011 On a price formation free boundary model by Lasry and Lions: the Neumann problem. Zbl 1233.91336 Caffarelli, Luis A.; Markowich, Peter A.; Wolfram, Marie-Therese 8 2011 Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Zbl 1204.35063 Caffarelli, Luis A.; Vasseur, Alexis 532 2010 Nonlocal minimal surfaces. Zbl 1248.53009 Caffarelli, L.; Roquejoffre, J.-M.; Savin, O. 260 2010 Variational problems with free boundaries for the fractional Laplacian. Zbl 1221.35453 Caffarelli, Luis A.; Roquejoffre, Jean-Michel; Sire, Yannick 174 2010 Free boundaries in optimal transport and Monge-Ampère obstacle problems. Zbl 1196.35231 Caffarelli, Luis A.; McCann, Robert J. 64 2010 Rates of convergence for the homogenization of fully nonlinear uniformly elliptic PDE in random media. Zbl 1192.35048 Caffarelli, Luis A.; Souganidis, Panagiotis E. 53 2010 Convergence of nonlocal threshold dynamics approximations to front propagation. Zbl 1190.65132 Caffarelli, Luis A.; Souganidis, Panagiotis E. 48 2010 Continuity of the temperature in boundary heat control problems. Zbl 1190.35125 Athanasopoulos, I.; Caffarelli, L. A. 45 2010 The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. Zbl 1210.76039 Caffarelli, Luis A.; Vasseur, Alexis F. 20 2010 Distance functions and almost global solutions of eikonal equations. Zbl 1187.35024 Caffarelli, Luis A.; Crandall, Michael G. 17 2010 Analysis on the junctions of domain walls. Zbl 1193.35255 Caffarelli, Luis A.; Lin, Fang Hua 10 2010 Smooth approximations of solutions to nonconvex fully nonlinear elliptic equations. Zbl 1208.35047 Caffarelli, Luis; Silvestre, Luis 9 2010 On the Evans-Krylov theorem. Zbl 1180.35229 Caffarelli, Luis; Silvestre, Luis 9 2010 Regularity theory for fully nonlinear integro-differential equations. Zbl 1170.45006 Caffarelli, Luis; Silvestre, Luis 359 2009 Some remarks on singular solutions of nonlinear elliptic equations. I. Zbl 1215.35068 Caffarelli, Luis; Li, Yan Yan; Nirenberg, Louis 40 2009 The geometry of solutions to a segregation problem for nondivergence systems. Zbl 1217.35015 Caffarelli, L. A.; Karakhanyan, A. L.; Lin, Fang-Hua 32 2009 Nonlocal heat flows preserving the \(L^2\) energy. Zbl 1154.35364 Caffarelli, Luis; Lin, Fanghua 24 2009 Random homogenization of an obstacle problem. Zbl 1180.35069 Caffarelli, L. A.; Mellet, A. 22 2009 Surfaces minimizing nonlocal energies. Zbl 1182.53055 Caffarelli, Luis A. 14 2009 Reflector problem in \({\mathbb R^n}\) endowed with non-Euclidean norm. Zbl 1173.78003 Caffarelli, Luis A.; Huang, Qingbo 6 2009 Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Zbl 1148.35097 Caffarelli, Luis A.; Salsa, Sandro; Silvestre, Luis 325 2008 Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. Zbl 1194.35138 Caffarelli, L. A.; Lin, Fang-Hua 82 2008 The structure of the free boundary for lower dimensional obstacle problems. Zbl 1185.35339 Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S. 79 2008 A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs. Zbl 1140.65075 Caffarelli, Luis A.; Souganidis, Panagiotis E. 41 2008 Weak solutions of one inverse problem in geometric optics. Zbl 1202.78003 Caffarelli, L. A.; Oliker, V. I. 26 2008 On the regularity of reflector antennas. Zbl 1140.35009 Caffarelli, Luis A.; Gutiíerrez, Cristian E.; Huang, Qingbo 24 2008 Random homogenization of fractional obstacle problems. Zbl 1156.74359 Caffarelli, Luis; Mellet, Antoine 15 2008 Some nonlinear problems involving nonlocal diffusions. Zbl 1419.35203 Caffarelli, Luis A. 15 2008 A counterexample to \(C^{2,1}\) regularity for parabolic fully nonlinear equations. Zbl 1162.35042 Caffarelli, Luis A.; Stefanelli, Ulisse 12 2008 Numerical solution of the Dirichlet problem for a Pucci equation in dimension two. Application to homogenization. Zbl 1155.65097 Caffarelli, L. A.; Glowinski, R. 7 2008 Viscosity method for homogenization of highly oscillating obstacles. Zbl 1158.35109 Caffarelli, Luis; Lee, Ki-Ahm 7 2008 An extension problem related to the fractional Laplacian. Zbl 1143.26002 Caffarelli, Luis; Silvestre, Luis 1,809 2007 ...and 190 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 7,639 Authors 131 Caffarelli, Luis Ángel 129 Valdinoci, Enrico 82 Byun, Sun-Sig 81 Vazquez, Juan Luis 74 Wei, Juncheng 72 Shahgholian, Henrik 69 Dipierro, Serena 60 Savin, Ovidiu V. 58 Wang, Lihe 57 Lee, Ki-Ahm 57 Zhang, Binlin 56 Sire, Yannick 54 Figalli, Alessio 49 Li, YanYan 49 Quaas, Alexander 48 Lin, Chang-Shou 48 Xiang, Mingqi 47 Ambrosio, Vincenzo 46 Bao, Jiguang 45 Garofalo, Nicola 44 Dong, Hongjie 42 Rădulescu, Vicenţiu D. 42 Rossi, Julio Daniel 40 Novaga, Matteo 39 Teixeira, Eduardo V. 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