Luis Caffarelli
- Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
1989/04/01 by Luis Caffarelli, Luis A. Caffarelli, Basilis Gidas +1 · 116 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
- The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian
1985/01/01 by Luis Caffarelli, L. Caffarelli, L. Nirenberg +3 · 70 citations
Mathematics · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
- Variational problems with two phases and their free boundaries
1984/01/01 by Hans Wilhelm Alt, Luis A. Caffarelli, Luis Caffarelli +1 · 38 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Contact Mechanics and Variational Inequalities #Advanced Mathematical Modeling in Engineering
- Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
2007/10/26 by Luis Caffarelli, Luis A. Caffarelli, Sandro Salsa +2 · 46 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Spectral Theory in Mathematical Physics
- Boundary regularity of maps with convex potentials
1992/10/01 by Luis Caffarelli, Luis A. Caffarelli · 24 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Advanced Mathematical Modeling in Engineering
- Boundary Regularity of Maps with Convex Potentials--II
1996/11/01 by Luis A. Caffarelli, Luis Caffarelli · 20 citations
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
- Some New Monotonicity Theorems with Applications to Free Boundary Problems
2002/03/01 by Luis Caffarelli, Luis A. Caffarelli, David Jerison +1 · 15 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Contact Mechanics and Variational Inequalities
- Free boundaries in optimal transport and Monge-Ampère obstacle problems
2010/03/25 by Luis Caffarelli, Robert McCann, Robert J. McCann · 14 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
- The Evans-Krylov theorem for nonlocal fully nonlinear equations
2011/07/29 by Luis Caffarelli, Luis Silvestre, Luís Silvestre · 17 citations
Engineering · Computer Science · Mathematics · #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering #Nonlinear Differential Equations Analysis
- Nonlocal minimal surfaces
2009/05/08 by Luis Caffarelli, Jean -Michel Roquejoffre, Caffarelli, L. A. +3 · 11 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
- Asymptotic estimates for the plasma problem
1980/09/01 by Luis A. Caffarelli, Luis Caffarelli, Avner Friedman · 7 citations
Mathematics · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #advanced mathematical theories
- Non-local gradient dependent operators
2012/05/16 by Clayton Bjorland, C. Bjorland, L. Caffarelli +3 · 8 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Advanced Mathematical Modeling in Engineering
- Regularity results for nonlocal equations by approximation
2009/02/23 by Luis Caffarelli, Caffarelli, Luis, Luís Silvestre +1 · 5 citations
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics
- Local Analysis of Solutions of Fractional Semi-Linear Elliptic Equations with Isolated Singularities
2014/02/18 by Luis Caffarelli, Tianling Jin, Yannick Sire +1 · 6 citations
Mathematics · #Nonlinear Partial Differential Equations #Nonlinear Differential Equations Analysis #Fractional Differential Equations Solutions
- Uniform Hölder Estimates in a Class of Elliptic Systems and Applications to Singular Limits in Models for Diffusion Flames
2006/09/12 by Luis Caffarelli, Luis A. Caffarelli, Jean-Michel Roquejoffre +1 · 4 citations
Mathematics · Computer Science · #Differential Equations and Numerical Methods #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering
- Asymptotic behaviour of a porous medium equation with fractional\n diffusion
2010/04/07 by Luis Caffarelli, Caffarelli, Luis, Vazquez, Juan Luis · 3 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Fractional Differential Equations Solutions #Advanced Mathematical Modeling in Engineering
- Some remarks on singular solutions of nonlinear elliptic equations. III:\n viscosity solutions, including parabolic operators
2011/01/14 by Luis Caffarelli, Yanyan Li, Caffarelli, Luis +3 · 2 citations
Computer Science · Mathematics · #35J60 #35J69 #53C21 #58J05 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations
- Regularity properties of nonlocal minimal surfaces via limiting arguments
2011/05/05 by Luis Caffarelli, Caffarelli, Luis, Enrico Valdinoci +1 · 2 citations
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations
- The structure of the free boundary for lower dimensional obstacle problems
2006/09/01 by Ioannis Athanasopoulos, Athanasopoulos, I., Luis Caffarelli +3 · 1 citation
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations
- A Free Boundary Problem Related to Thermal Insulation
2015/11/18 by Luis Caffarelli, Dennis Kriventsov, Caffarelli, Luis A. +1 · 1 citation
Computer Science · Engineering · #35A01 #35R35 #49J45 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics
- Optimal regularity and structure of the free boundary for minimizers in\n cohesive zone models
2017/12/21 by Luis Caffarelli, Caffarelli, Luis, Filippo Cagnetti +3 · 1 citation
Computer Science · Engineering · Mathematics · #35B65 #35R35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Nonlinear Partial Differential Equations
- Regularity theory for nonlinear integral operators
2010/03/08 by Luis Caffarelli, Chi Hin Chan, Caffarelli, Luis +3 · 1 citation
Computer Science · Mathematics · #35B65 #45G05 #47G10. #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
- On the Grad-Mercier equation and Semilinear Free Boundary Problems
2025/04/17 by Luis Caffarelli, Antonio Farah, Caffarelli, Luis +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations