Edit Profile Caffarelli, Luis Ángel Compute Distance To: Compute Author ID: caffarelli.luis-a Published as: Caffarelli, Luis A.; Caffarelli, Luis; Caffarelli, L. A.; Caffarelli, L.; Caffarelli, Luis Ángel; Cafferelli, L. A. Homepage: http://www.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) Documents Indexed: 308 Publications since 1974, including 8 Books Biographic References: 1 Publication all top 5 Co-Authors 58 single-authored 43 Friedman, Avner 18 Nirenberg, Louis 13 Spruck, Joel 12 Alt, Hans Wilhelm 12 Athanasopoulos, Ioannis 11 Salsa, Sandro 10 Silvestre, Luis E. 8 Mellet, Antoine 8 Vazquez, Juan Luis 6 Li, YanYan 6 Markowich, Peter Alexander 6 Sire, Yannick 6 Vasseur, Alexis F. 5 Berestycki, Henri 5 Kenig, Carlos Eduardo 5 Lee, Ki-Ahm 5 Lin, Fang Hua 5 Riviere, Nestor M. 5 Roquejoffre, Jean-Michel 5 Savin, Ovidiu V. 5 Shahgholian, Henrik 5 Valdinoci, Enrico 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 Arapostathis, Aristotle 3 Burger, Martin 3 De Silva, Daniela 3 Huang, Qingbo 3 Jerison, David S. 3 Wolfram, Marie-Therese 2 Allen, Mark G. 2 Ambrosio, Luigi 2 Biswas, Anup 2 Bjorland, Clayton 2 Bonforte, Matteo 2 Calderón, Calixto Pedro 2 de la Llave, Rafael 2 Fabes, Eugene B. 2 Gidas, Basilis 2 Grillo, Gabriele 2 Karakhanyan, Aram L. 2 Kohn, Robert Vita 2 Lederman, Claudia B. 2 McCann, Robert J. 2 Milakis, Emmanouil 2 Milman, Mario Marcos 2 Oliker, Vladimir I. 2 Patrizi, Stefania 2 Quitalo, Veronica 2 Salazar, Jorge A. 2 Stinga, Pablo Raúl 2 Torelli, Alessandro 2 Urbano, José Miguel 1 Brenier, Yann 1 Brézis, Haïm 1 Brezzi, Franco 1 Buttazzo, Giuseppe 1 Cagnetti, Filippo 1 Chan, Chi Hin 1 Charro, Fernando 1 Dávila, Gonzalo 1 Dipierro, Serena 1 Dolbeault, Jean 1 E, Weinan 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 1 Kinderlehrer, David 1 Kocan, Maciej 1 Kochengin, Sergey A. 1 Kohn, Joseph J. 1 Kriventsov, Dennis 1 Leitão, Raimundo A. 1 Lieb, Elliott H. 1 Littman, Walter 1 Ma, Xi-Nan 1 Manasevich, Raul F. 1 Maugeri, Antonino 1 Monneau, Régis 1 Mortola, Stefano 1 Muler, Nora E. 1 Nguyen, Truyen Van 1 Pang, Guodong 1 Peral Alonso, Ireneo ...and 26 more Co-Authors all top 5 Serials 35 Communications on Pure and Applied Mathematics 21 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 5 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 4 American Journal of Mathematics 4 Calculus of Variations and Partial Differential Equations 4 Discrete and Continuous Dynamical Systems 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 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 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 Annals of PDE 1 Philosophical Transactions A. Royal Society of London all top 5 Fields 255 Partial differential equations (35-XX) 68 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 Operator theory (47-XX) 11 Global analysis, analysis on manifolds (58-XX) 11 Mechanics of deformable solids (74-XX) 10 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 Optics, electromagnetic theory (78-XX) 7 Real functions (26-XX) 7 Functional analysis (46-XX) 7 Numerical analysis (65-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Probability theory and stochastic processes (60-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Integral equations (45-XX) 4 History and biography (01-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 271 Publications have been cited 13,618 times in 7,901 Documents Cited by ▼ Year ▼ An extension problem related to the fractional Laplacian. Zbl 1143.26002Caffarelli, Luis; Silvestre, Luis 1,171 2007 Partial regularity of suitable weak solutions of the Navier-Stokes equations. Zbl 0509.35067Caffarelli, L.; Kohn, R.; Nirenberg, Louis 569 1982 Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Zbl 0702.35085Caffarelli, Luis A.; Gidas, Basilis; Spruck, Joel 499 1989 Fully nonlinear elliptic equations. Zbl 0834.35002Caffarelli, Luis A.; Cabré, Xavier 479 1995 First order interpolation inequalities with weights. Zbl 0563.46024Caffarelli, L.; Kohn, R.; Nirenberg, Louis 477 1984 Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Zbl 1204.35063Caffarelli, Luis A.; Vasseur, Alexis 367 2010 The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian. Zbl 0654.35031Caffarelli, L.; Nirenberg, L.; Spruck, J. 330 1985 Existence and regularity for a minimum problem with free boundary. Zbl 0449.35105Alt, H. W.; Caffarelli, L. A. 292 1981 Interior a priori estimates for solutions of fully nonlinear equations. Zbl 0692.35017Caffarelli, Luis A. 266 1989 On \(W^{1,p}\) estimates for elliptic equations in divergence form. Zbl 0906.35030Caffarelli, L. A.; Peral, I. 245 1998 Regularity theory for fully nonlinear integro-differential equations. Zbl 1170.45006Caffarelli, Luis; Silvestre, Luis 244 2009 The Dirichlet problem for nonlinear second-order elliptic equations. I: Monge-Ampère equation. Zbl 0598.35047Caffarelli, L.; Nirenberg, Louis; Spruck, J. 238 1984 Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Zbl 1148.35097Caffarelli, Luis A.; Salsa, Sandro; Silvestre, Luis 235 2008 Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation. Zbl 0704.35044Caffarelli, Luis A. 180 1990 Variational problems with two phases and their free boundary. Zbl 0844.35137Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 174 1984 Nonlocal minimal surfaces. Zbl 1248.53009Caffarelli, L.; Roquejoffre, J.-M.; Savin, O. 174 2010 The obstacle problem revisited. Zbl 0928.49030Caffarelli, L. A. 164 1998 Non-local diffusions, drifts and games. Zbl 1266.35060Caffarelli, Luis 148 2012 A geometric approach to free boundary problems. Zbl 1083.35001Caffarelli, Luis; Salsa, Sandro 146 2005 Boundary behavior of nonnegative solutions of elliptic operators in divergence form. Zbl 0512.35038Caffarelli, L.; Fabes, E.; Mortola, S.; Salsa, S. 144 1981 The regularity of free boundaries in higher dimensions. Zbl 0386.35046Caffarelli, Luis A. 141 1978 On viscosity solutions of fully nonlinear equations with measurable ingredients. Zbl 0854.35032Caffarelli, L.; Crandall, M. G.; Kocan, M.; Świȩch, A. 140 1996 A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity. Zbl 0704.35045Caffarelli, L. A. 122 1990 Further qualitative properties for elliptic equations in unbounded domains. Zbl 1079.35513Berestycki, Henri; Caffarelli, Luis; Nirenberg, Louis 121 1997 Variational problems with free boundaries for the fractional Laplacian. Zbl 1221.35453Caffarelli, Luis A.; Roquejoffre, Jean-Michel; Sire, Yannick 120 2010 The Dirichlet problem for nonlinear second-order elliptic equations. II: Complex Monge-Ampère, and uniformly elliptic, equations. Zbl 0598.35048Caffarelli, L.; Kohn, J. J.; Nirenberg, Louis; Spruck, J. 116 1985 Monotonicity for elliptic equations in unbounded Lipschitz domains. Zbl 0906.35035Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 114 1997 The regularity of mappings with a convex potential. Zbl 0753.35031Caffarelli, Luis A. 110 1992 Vortex condensation in the Chern-Simons Higgs model: An existence theorem. Zbl 0846.58063Caffarelli, Luis A.; Yang, Yisong 106 1995 Regularity results for nonlocal equations by approximation. Zbl 1231.35284Caffarelli, Luis; Silvestre, Luis 103 2011 Some regularity properties of solutions of Monge Ampère equation. Zbl 0761.35028Caffarelli, Luis A. 101 1991 A Harnack inequality approach to the regularity of free boundaries. II: Flat free boundaries are Lipschitz. Zbl 0676.35086Caffarelli, Luis A. 97 1989 A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are \(C^{1,\alpha}\). Zbl 0676.35085Caffarelli, Luis A. 96 1987 Convexity of solutions of semilinear elliptic equations. Zbl 0599.35065Caffarelli, Luis A.; Friedman, Avner 92 1985 Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105Caffarelli, Luis; Vazquez, Juan Luis 91 2011 Convexity properties of solutions to some classical variational problems. Zbl 0508.49013Caffarelli, Luis A.; Spruck, Joel 89 1982 The initial trace of a solution of the porous medium equation. Zbl 0556.76084Aronson, D. G.; Caffarelli, L. A. 82 1983 Fractional elliptic equations, Caccioppoli estimates and regularity. Zbl 1381.35211Caffarelli, Luis A.; Stinga, Pablo Raúl 81 2016 Inequalities for second-order elliptic equations with applications to unbounded domains. I. Zbl 0860.35004Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 80 1996 Boundary regularity of maps with convex potentials. II. Zbl 0916.35016Caffarelli, Luis A. 80 1996 Properties of the solutions of the linearized Monge-Ampère equation. Zbl 0878.35039Caffarelli, Luis A.; Gutiérrez, Cristian E. 76 1997 A parabolic problem with a fractional time derivative. Zbl 1338.35428Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 74 2016 Uniform estimates and limiting arguments for nonlocal minimal surfaces. Zbl 1357.49143Caffarelli, Luis; Valdinoci, Enrico 74 2011 Regularity of the free boundary of a gas flow in an \(n\)-dimensional porous medium. Zbl 0439.76085Caffarelli, Luis A.; Friedman, Avner 69 1980 Boundary regularity of maps with convex potentials. Zbl 0778.35015Caffarelli, Luis A. 69 1992 Nonlinear second-order elliptic equations. V: The Dirichlet problem for Weingarten hypersurfaces. Zbl 0672.35028Caffarelli, Luis; Nirenberg, Louis; Spruck, Joel 67 1988 The Evans-Krylov theorem for nonlocal fully nonlinear equations. Zbl 1232.49043Caffarelli, Luis; Silvestre, Luis 66 2011 Regularity theory for parabolic nonlinear integral operators. Zbl 1223.35098Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis 65 2011 Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs. Zbl 1053.49032Caffarelli, Luis A.; Feldman, Mikhail; McCann, Robert J. 64 2002 Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. Zbl 1194.35138Caffarelli, L. A.; Lin, Fang-Hua 64 2008 Continuity of the temperature in the two-phase Stefan problem. Zbl 0516.35080Caffarelli, L. A.; Evans, L. C. 61 1983 Regularity of a free boundary with application to the Pompeiu problem. Zbl 0960.35112Caffarelli, Luis A.; Karp, Lavi; Shahgholian, Henrik 61 2000 A Harnack inequality approach to the regularity of free boundaries. III: Existence theory, compactness, and dependence on X. Zbl 0702.35249Caffarelli, Luis A. 60 1988 Further regularity for the Signorini problem. Zbl 0427.35019Caffarelli, L. A. 58 1979 Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media. Zbl 1063.35025Caffarelli, Luis A.; Souganidis, Panagiotis E.; Wang, L. 57 2005 Lipschitz continuity of solutions and interfaces of the N-dimensional porous medium equation. Zbl 0644.35058Caffarelli, L. A.; Vazquez, J. L.; Wolanski, N. I. 54 1987 Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations. Zbl 0593.35047Caffarelli, Luis A.; Friedman, Avner 53 1985 Monotonicity properties of optimal transportation and the FKG and related inequalities. Zbl 0978.60107Caffarelli, Luis A. 53 2000 An extension to a theorem of Jörgens, Calabi, and Pogorelov. Zbl 1236.35041Caffarelli, L.; Li, YanYan 52 2003 Uniform estimates for regularization of free boundary problems. Zbl 0702.35252Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 52 1990 A free boundary problem for quasi-linear elliptic equations. Zbl 0554.35129Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 51 1984 An \(L^ \infty\) bound for solutions of the Cahn-Hilliard equation. Zbl 0851.35010Caffarelli, Luis A.; Muler, Nora E. 51 1995 An optimal partition problem for eigenvalues. Zbl 1123.65060Cafferelli, L. A.; Lin, Fang Hua 51 2007 Optimal transportation and applications. Lectures given at the C. I. M. E. summer school, Martina Franca, Italy, September 2–8, 2001. Zbl 1013.00028Ambrosio, Luigi; Brenier, Yann; Buttazzo, Giusseppe; Caffarelli, Luis A.; Salsa, S. (ed.); Villani, Cédric 50 2003 A free-boundary problem for the heat equation arising in flame propagation. Zbl 0814.35149Caffarelli, Luis A.; Vázquez, Juan L. 49 1995 Some new monotonicity theorems with applications to free boundary problems. Zbl 1142.35382Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E. 49 2002 Uniform convergence of a singular perturbation problem. Zbl 0829.49013Caffarelli, Luis A.; Córdoba, Antonio 48 1995 Global energy minimizers for free boundary problems and full regularity in three dimensions. Zbl 1330.35545Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E. 48 2004 The structure of the free boundary for lower dimensional obstacle problems. Zbl 1185.35339Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S. 48 2008 Completely singular elliptic-harmonic measures. Zbl 0482.35020Caffarelli, Luis A.; Fabes, Eugene B.; Kenig, Carlos E. 47 1981 Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis 47 2013 The obstacle problem for the biharmonic operator. Zbl 0405.31007Caffarelli, Luis A.; Friedman, Avner 47 1979 Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio 46 2012 Non-local gradient dependent operators. Zbl 1252.35099Bjorland, C.; Caffarelli, L.; Figalli, A. 46 2012 Compactness methods in free boundary problems. Zbl 0437.35070Caffarelli, Luis A. 45 1980 Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088Caffarelli, Luis; Figalli, Alessio 45 2013 A gradient bound for entire solutions of quasi-linear equations and its consequences. Zbl 0819.35016Caffarelli, Luis; Garofalo, Nicola; Segala, Fausto 44 1994 Continuity of the density of a gas flow in a porous medium. Zbl 0425.35060Caffarelli, Luis A.; Friedman, Avner 44 1979 Regularity properties of nonlocal minimal surfaces via limiting arguments. Zbl 1284.53008Caffarelli, Luis; Valdinoci, Enrico 44 2013 Free boundaries in optimal transport and Monge-Ampère obstacle problems. Zbl 1196.35231Caffarelli, Luis A.; McCann, Robert J. 42 2010 Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043Caffarelli, Luis; Vázquez, Juan-Luis 42 2011 Rates of convergence for the homogenization of fully nonlinear uniformly elliptic PDE in random media. Zbl 1192.35048Caffarelli, Luis A.; Souganidis, Panagiotis E. 42 2010 Symmetry for elliptic equations in a half space. Zbl 0793.35034Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 41 1993 Real analysis related to the Monge-Ampère equation. Zbl 0858.35034Caffarelli, Luis A.; Gutiérrez, Cristian E. 41 1996 An optimization problem with volume constraint. Zbl 0588.49005Aguilera, N.; Alt, H. W.; Caffarelli, L. A. 40 1986 Regularity of a free boundary in parabolic potential theory. Zbl 1054.35142Caffarelli, Luis; Petrosyan, Arshak; Shahgholian, Henrik 40 2004 The blow-up boundary for nonlinear wave equations. Zbl 0638.35053Caffarelli, Luis A.; Friedman, Avner 40 1986 Allocation maps with general cost functions. Zbl 0883.49030Caffarelli, Luis A. 40 1996 Optimal regularity of lower dimensional obstacle problems. Zbl 1108.35038Athanasopoulos, I.; Caffarelli, L. A. 40 2004 Planelike minimizers in periodic media. Zbl 1036.49040Caffarelli, Luis A.; de la Llave, Rafael 39 2001 How an initially stationary interface begins to move in porous medium flow. Zbl 0542.76119Aronson, D. G.; Caffarelli, L. A.; Kamin, S. 38 1983 Nonlinear second order elliptic equations. IV. Starshaped compact Weingarten hypersurfaces. Zbl 0672.35027Caffarelli, L.; Nirenberg, L.; Spruck, J. 38 1986 Potential methods in variational inequalities. Zbl 0455.49010Caffarelli, L. A.; Kinderlehrer, D. 37 1980 Regularity of the free boundary in parabolic phase-transition problems. Zbl 0891.35164Athanasopoulos, I.; Caffarelli, L.; Salsa, S. 37 1996 Smoothness and analyticity of free boundaries in variational inequalities. Zbl 0363.35009Caffarelli, L. A.; Riviere, N. M. 37 1976 Continuity of the temperature in boundary heat control problems. Zbl 1190.35125Athanasopoulos, I.; Caffarelli, L. A. 37 2010 Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems. Zbl 0853.35049Athanasopoulos, I.; Caffarelli, L.; Salsa, S. 36 1996 Asymptotic estimates for the plasma problem. Zbl 0466.35033Caffarelli, Luis A.; Friedman, Avner 35 1980 On the case of equality in the Brunn-Minkowski inequality for capacity. Zbl 0847.31005Caffarelli, Luis A.; Jerison, David; Lieb, Elliott H. 35 1996 Regularity of the free boundary for the one-dimensional flow of gas in a porous medium. Zbl 0439.76084Caffarelli, Luis A.; Friedman, Avner 34 1979 Regularity for \(C^{1, \alpha}\) interface transmission problems. Zbl 1467.35169Caffarelli, Luis Ángel; Soria-Carro, María; Stinga, Pablo Raúl 2 2021 Minimal surfaces and free boundaries: recent developments. Zbl 1433.35464Caffarelli, Luis A.; Sire, Yannick 1 2020 Fully nonlinear integro-differential equations with deforming kernels. Zbl 1452.35055Caffarelli, Luis; Teymurazyan, Rafayel; Urbano, José Miguel 1 2020 Optimal regularity and structure of the free boundary for minimizers in cohesive zone models. Zbl 1442.49005Caffarelli, L.; Cagnetti, F.; Figalli, A. 1 2020 Existence of weak solutions to a continuity equation with space time nonlocal Darcy law. Zbl 1459.35233Caffarelli, Luis; Gualdani, Maria; Zamponi, Nicola 1 2020 Parabolic obstacle problems, quasi-convexity and regularity. Zbl 1432.35264Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil 3 2019 Ergodic control of a class of jump diffusions with finite Lévy measures and rough kernels. Zbl 1415.93288Arapostathis, Ari; Caffarelli, Luis; Pang, Guodong; Zheng, Yi 3 2019 On uniqueness of solutions to viscous HJB equations with a subquadratic nonlinearity in the gradient. Zbl 1428.35125Arapostathis, Ari; Biswas, Anup; Caffarelli, Luis 1 2019 Interior regularity for fractional systems. Zbl 1411.35111Caffarelli, Luis; Dávila, Gonzalo 1 2019 On the regularity of the non-dynamic parabolic fractional obstacle problem. Zbl 1394.35588Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil 10 2018 A minimization problem with free boundary related to a cooperative system. Zbl 1395.35226Caffarelli, Luis A.; Shahgholian, Henrik; Yeressian, Karen 7 2018 Bounds on the Green function for integral operators and fractional harmonic measure with applications to boundary Harnack. Zbl 1387.35071Caffarelli, Luis A.; Sire, Yannick 3 2018 Two-phase anisotropic free boundary problems and applications to the Bellman equation in 2D. Zbl 1393.35247Caffarelli, L.; De Silva, D.; Savin, O. 2 2018 Obstacle problems for integro-differential operators: regularity of solutions and free boundaries. Zbl 1371.35361Caffarelli, Luis; Ros-Oton, Xavier; Serra, Joaquim 28 2017 Porous medium flow with both a fractional potential pressure and fractional time derivative. Zbl 1372.35328Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 19 2017 On some pointwise inequalities involving nonlocal operators. Zbl 06703883Caffarelli, Luis A.; Sire, Yannick 15 2017 A logistic equation with nonlocal interactions. Zbl 1356.35261Caffarelli, Luis; Dipierro, Serena; Valdinoci, Enrico 12 2017 The two membranes problem for different operators. Zbl 1368.35045Caffarelli, L.; De Silva, D.; Savin, O. 9 2017 On a long range segregation model. Zbl 1386.35084Caffarelli, L.; Patrizi, S.; Quitalo, V. 4 2017 Fractional elliptic equations, Caccioppoli estimates and regularity. Zbl 1381.35211Caffarelli, Luis A.; Stinga, Pablo Raúl 81 2016 A parabolic problem with a fractional time derivative. Zbl 1338.35428Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 74 2016 A free boundary problem related to thermal insulation. Zbl 1351.35268Caffarelli, Luis A.; Kriventsov, Dennis 12 2016 Obstacle-type problems for minimal surfaces. Zbl 1370.35070Caffarelli, L.; De Silva, D.; Savin, O. 11 2016 The Dirichlet problem for stable-like operators and related probabilistic representations. Zbl 1352.60080Arapostathis, Ari; Biswas, Anup; Caffarelli, Luis 10 2016 Regularity of solutions of the fractional porous medium flow with exponent \(1/2\). Zbl 1335.35273Caffarelli, L.; Vázquez, J. L. 8 2016 A non-local Monge-Ampère equation. Zbl 1361.35067Caffarelli, Luis; Silvestre, Luis 5 2016 Minimization of a fractional perimeter-Dirichlet integral functional. Zbl 1323.35216Caffarelli, Luis; Savin, Ovidiu; Valdinoci, Enrico 14 2015 On a fractional Monge-Ampère operator. Zbl 1393.35268Caffarelli, Luis; Charro, Fernando 8 2015 Regularity of free boundaries a heuristic retro. Zbl 1353.35319Caffarelli, Luis A.; Shahgholian, Henrik 4 2015 A bifurcation phenomenon in a singularly perturbed one-phase free boundary problem of phase transition. Zbl 1334.35439Caffarelli, Luis A.; Wang, Peiyong 2 2015 Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities. Zbl 1296.35208Caffarelli, Luis; Jin, Tianling; Sire, Yannick; Xiong, Jingang 26 2014 Partial differential equation models in the socio-economic sciences. Zbl 1353.00004Burger, Martin; Caffarelli, Luis; Markowich, Peter A. 13 2014 Hölder regularity for generalized master equations with rough kernels. Zbl 1312.45013Caffarelli, Luis; Silvestre, Luis 11 2014 On the asymptotic behavior of a Boltzmann-type price formation model. Zbl 1307.35302Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 8 2014 Regularity for anisotropic fully nonlinear integro-differential equations. Zbl 1304.35730Caffarelli, Luis A.; Leitão, Raimundo; Urbano, José Miguel 5 2014 Counter-example in three dimension and homogenization of geometric motions in two dimension. Zbl 1293.35026Caffarelli, L. A.; Monneau, R. 5 2014 A perturbation argument for a Monge-Ampère type equation arising in optimal transportation. Zbl 1294.35170Caffarelli, Luis; Del Mar González, María; Nguyen, Truyen 4 2014 Relations between geometric convexity, doubling measures and property \(\Gamma\). Zbl 1307.46006Caffarelli, Luis A.; Crandall, Michael G. 1 2014 Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis 47 2013 Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088Caffarelli, Luis; Figalli, Alessio 45 2013 Regularity properties of nonlocal minimal surfaces via limiting arguments. Zbl 1284.53008Caffarelli, Luis; Valdinoci, Enrico 44 2013 Some remarks on singular solutions of nonlinear elliptic equations. III: Viscosity solutions including parabolic operators. Zbl 1279.35044Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis 31 2013 On a Boltzmann-type price formation model. Zbl 1372.91039Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 17 2013 A priori bounds for solutions of a nonlocal evolution PDE. Zbl 1273.35067Caffarelli, Luis; Valdinoci, Enrico 2 2013 Non-local diffusions, drifts and games. Zbl 1266.35060Caffarelli, Luis 148 2012 Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio 46 2012 Non-local gradient dependent operators. Zbl 1252.35099Bjorland, C.; Caffarelli, L.; Figalli, A. 46 2012 Some remarks on singular solutions of nonlinear elliptic equations. II: Symmetry and monotonicity via moving planes. Zbl 1325.35044Caffarelli, Luis; Li, YanYan; Nirenberg, Louis 16 2012 Traveling waves for a boundary reaction-diffusion equation. Zbl 1255.35072Caffarelli, L.; Mellet, A.; Sire, Y. 6 2012 The De Giorgi method for nonlocal fluid dynamics. Zbl 1357.35249Caffarelli, Luis A.; Vasseur, Alexis 5 2012 The problem of two sticks. Zbl 1257.46009Caffarelli, Luis A.; Crandall, Michael G. 1 2012 Regularity results for nonlocal equations by approximation. Zbl 1231.35284Caffarelli, Luis; Silvestre, Luis 103 2011 Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105Caffarelli, Luis; Vazquez, Juan Luis 91 2011 Uniform estimates and limiting arguments for nonlocal minimal surfaces. Zbl 1357.49143Caffarelli, Luis; Valdinoci, Enrico 74 2011 The Evans-Krylov theorem for nonlocal fully nonlinear equations. Zbl 1232.49043Caffarelli, Luis; Silvestre, Luis 66 2011 Regularity theory for parabolic nonlinear integral operators. Zbl 1223.35098Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis 65 2011 Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043Caffarelli, Luis; Vázquez, Juan-Luis 42 2011 On a price formation free boundary model by Lasry and Lions. Zbl 1216.91012Caffarelli, Luis A.; Markowich, Peter A.; Pietschmann, Jan-F. 12 2011 On a price formation free boundary model by Lasry and Lions: the Neumann problem. Zbl 1233.91336Caffarelli, Luis A.; Markowich, Peter A.; Wolfram, Marie-Therese 7 2011 Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Zbl 1204.35063Caffarelli, Luis A.; Vasseur, Alexis 367 2010 Nonlocal minimal surfaces. Zbl 1248.53009Caffarelli, L.; Roquejoffre, J.-M.; Savin, O. 174 2010 Variational problems with free boundaries for the fractional Laplacian. Zbl 1221.35453Caffarelli, Luis A.; Roquejoffre, Jean-Michel; Sire, Yannick 120 2010 Free boundaries in optimal transport and Monge-Ampère obstacle problems. Zbl 1196.35231Caffarelli, Luis A.; McCann, Robert J. 42 2010 Rates of convergence for the homogenization of fully nonlinear uniformly elliptic PDE in random media. Zbl 1192.35048Caffarelli, Luis A.; Souganidis, Panagiotis E. 42 2010 Continuity of the temperature in boundary heat control problems. Zbl 1190.35125Athanasopoulos, I.; Caffarelli, L. A. 37 2010 Convergence of nonlocal threshold dynamics approximations to front propagation. Zbl 1190.65132Caffarelli, Luis A.; Souganidis, Panagiotis E. 30 2010 The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. Zbl 1210.76039Caffarelli, Luis A.; Vasseur, Alexis F. 16 2010 Distance functions and almost global solutions of eikonal equations. Zbl 1187.35024Caffarelli, Luis A.; Crandall, Michael G. 15 2010 Analysis on the junctions of domain walls. Zbl 1193.35255Caffarelli, Luis A.; Lin, Fang Hua 8 2010 On the Evans-Krylov theorem. Zbl 1180.35229Caffarelli, Luis; Silvestre, Luis 8 2010 Smooth approximations of solutions to nonconvex fully nonlinear elliptic equations. Zbl 1208.35047Caffarelli, Luis; Silvestre, Luis 7 2010 Regularity theory for fully nonlinear integro-differential equations. Zbl 1170.45006Caffarelli, Luis; Silvestre, Luis 244 2009 Some remarks on singular solutions of nonlinear elliptic equations. I. Zbl 1215.35068Caffarelli, Luis; Li, Yan Yan; Nirenberg, Louis 27 2009 The geometry of solutions to a segregation problem for nondivergence systems. Zbl 1217.35015Caffarelli, L. A.; Karakhanyan, A. L.; Lin, Fang-Hua 25 2009 Nonlocal heat flows preserving the \(L^2\) energy. Zbl 1154.35364Caffarelli, Luis; Lin, Fanghua 17 2009 Random homogenization of an obstacle problem. Zbl 1180.35069Caffarelli, L. A.; Mellet, A. 14 2009 Surfaces minimizing nonlocal energies. Zbl 1182.53055Caffarelli, Luis A. 10 2009 Reflector problem in \({\mathbb R^n}\) endowed with non-Euclidean norm. Zbl 1173.78003Caffarelli, Luis A.; Huang, Qingbo 4 2009 Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Zbl 1148.35097Caffarelli, Luis A.; Salsa, Sandro; Silvestre, Luis 235 2008 Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. Zbl 1194.35138Caffarelli, L. A.; Lin, Fang-Hua 64 2008 The structure of the free boundary for lower dimensional obstacle problems. Zbl 1185.35339Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S. 48 2008 A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs. Zbl 1140.65075Caffarelli, Luis A.; Souganidis, Panagiotis E. 32 2008 Weak solutions of one inverse problem in geometric optics. Zbl 1202.78003Caffarelli, L. A.; Oliker, V. I. 20 2008 On the regularity of reflector antennas. Zbl 1140.35009Caffarelli, Luis A.; Gutiíerrez, Cristian E.; Huang, Qingbo 20 2008 Random homogenization of fractional obstacle problems. Zbl 1156.74359Caffarelli, Luis; Mellet, Antoine 10 2008 A counterexample to \(C^{2,1}\) regularity for parabolic fully nonlinear equations. Zbl 1162.35042Caffarelli, Luis A.; Stefanelli, Ulisse 9 2008 Numerical solution of the Dirichlet problem for a Pucci equation in dimension two. Application to homogenization. Zbl 1155.65097Caffarelli, L. A.; Glowinski, R. 5 2008 Viscosity method for homogenization of highly oscillating obstacles. Zbl 1158.35109Caffarelli, Luis; Lee, Ki-Ahm 3 2008 Some nonlinear problems involving nonlocal diffusions. Zbl 1419.35203Caffarelli, Luis A. 3 2008 An extension problem related to the fractional Laplacian. Zbl 1143.26002Caffarelli, Luis; Silvestre, Luis 1,171 2007 An optimal partition problem for eigenvalues. Zbl 1123.65060Cafferelli, L. A.; Lin, Fang Hua 51 2007 A constant rank theorem for solutions of fully nonlinear elliptic equations. Zbl 1191.35127Caffarelli, Luis A.; Guan, Pengfei; Ma, Xinan 29 2007 Uniform Hölder estimates in a class of elliptic systems and applications to singular limits in models for diffusion flames. Zbl 1189.35084Caffarelli, Luis A.; Roquejoffre, Jean-Michel 18 2007 Capillary drops: contact angle hysteresis and sticking drops. Zbl 1168.76007Caffarelli, L. A.; Mellet, A. 16 2007 Capillary drops on an inhomogeneous surface. Zbl 1200.76053Caffarelli, L. A.; Mellet, A. 9 2007 Homogenization of oscillating free boundaries: the elliptic case. Zbl 1122.35156Caffarelli, L.; Lee, K. 6 2007 Flame propagation in one-dimensional stationary ergodic media. Zbl 1110.76054Caffarelli, L. A.; Lee, K.-A.; Mellet, A. 3 2007 Free boundary problems for fractional powers of the Laplacian. Zbl 1253.35224Caffarelli, Luis 1 2007 Phase transitions: uniform regularity of the intermediate layers. Zbl 1090.49019Caffarelli, Luis A.; Córdoba, Antonio 19 2006 Homogenization and flame propagation in periodic excitable media: the asymptotic speed of propagation. Zbl 1093.35010Caffarelli, L. A.; Lee, K.-A.; Mellet, A. 17 2006 ...and 171 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 5,645 Authors 121 Caffarelli, Luis Ángel 102 Valdinoci, Enrico 76 Vazquez, Juan Luis 60 Wei, Juncheng 58 Byun, Sun-Sig 56 Shahgholian, Henrik 56 Wang, Lihe 49 Figalli, Alessio 48 Lin, Chang-Shou 46 Sire, Yannick 45 Dipierro, Serena 45 Savin, Ovidiu V. 43 Zhang, Binlin 40 Quaas, Alexander 39 Ambrosio, Vincenzo 39 Li, YanYan 38 Lee, Ki-Ahm 38 Xiang, Mingqi 35 Friedman, Avner 33 Bao, Jiguang 33 Dong, Hongjie 33 Teixeira, Eduardo V. 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