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Mathematics
USA
2026

D-Index & Metrics

Mathematics

D-Index
99
Citations
39821
World Ranking
49
National Ranking
35

Research.com Recognitions

  • 2026 - Research.com Mathematics in United States Leader Award
  • 2025 - Research.com Mathematics in United States Leader Award
  • 2018 - SIAM Fellow For seminal contributions in regularity theory of nonlinear partial differential equations, free boundary problems, fully nonlinear equations, and nonlocal diffusion.
  • 2014 - Steele Prize for Seminal Contribution to Research
  • 2013 - Fellow of the American Mathematical Society
  • 2012 - Wolf Prize in Mathematics for his work on partial differential equations.
  • 2009 - Steele Prize for Lifetime Achievement
  • 2005 - Rolf Schock Prize for Mathematics
  • 1991 - Member of the National Academy of Sciences
  • 1986 - Fellow of the American Academy of Arts and Sciences

Overview

Luis A. Caffarelli is affiliated with The University of Texas at Austin in the United States and primarily works in the field of mathematics. Their scholarly contributions span several subfields including applied mathematics, computational theory and mathematics, mathematical physics, geometry and topology, and numerical analysis.

The main topics covered by their research include nonlinear partial differential equations, advanced mathematical modeling in engineering, geometric analysis and curvature flows, geometry and complex manifolds, differential equations and numerical methods, stochastic processes and statistical mechanics, and numerical methods in inverse problems.

Frequent venues for publication are:

  • arXiv (Cornell University)
  • Archive for Rational Mechanics and Analysis
  • Communications in Partial Differential Equations
  • Advances in Mathematics
  • Analysis & PDE

Some notable recent papers by Luis A. Caffarelli include:

  • Regularity for C1,α Interface Transmission Problems, 2021, Archive for Rational Mechanics and Analysis
  • The two-phase Stefan problem with anomalous diffusion, 2022, Advances in Mathematics
  • Global C1,α Regularity for Monge-Ampère Equation and Convex Envelope, 2022, Archive for Rational Mechanics and Analysis
  • On a family of fully nonlinear integrodifferential operators: from fractional Laplacian to nonlocal Monge-Ampère, 2024, Analysis & PDE
  • Existence of weak solutions to a continuity equation with space time nonlocal Darcy law, 2020, Communications in Partial Differential Equations

The most frequent co-authors collaborating with Luis A. Caffarelli include:

  • María Soria-Carro
  • Pablo Raúl Stinga
  • Ioannis Athanasopoulos
  • Emmanouil Milakis
  • Ignacio Tomasetti

Their contributions have been recognized through several awards, including:

  • SIAM Fellow (2018) for contributions in regularity theory of nonlinear partial differential equations, free boundary problems, fully nonlinear equations, and nonlocal diffusion
  • Steele Prize for Seminal Contribution to Research (2014)
  • Fellow of the American Mathematical Society (2013)
  • Wolf Prize in Mathematics (2012) for work on partial differential equations
  • Steele Prize for Lifetime Achievement (2009)
  • Rolf Schock Prize for Mathematics (2005)
  • Member of the National Academy of Sciences (1991)
  • Fellow of the American Academy of Arts and Sciences (1986)

Best Publications

  • An Extension Problem Related to the Fractional Laplacian

    Luis A Caffarelli;Luis Silvestre

  • Partial regularity of suitable weak solutions of the navier‐stokes equations

    L. Caffarelli;R. Kohn;L. Nirenberg

  • Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth

    Luis A. Caffarelli;Basilis Gidas;Joel Spruck

  • Fully Nonlinear Elliptic Equations

    Luis A. Caffarelli;Xavier Cabré

  • First order interpolation inequalities with weights

    L. Caffarelli;R. Kohn;L. Nirenberg

  • The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian

    L. Caffarelli;L. Nirenberg;J. Spruck

  • Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation

    Luis A. Caffarelli;Alexis Vasseur

  • Existence and regularity for a minimum problem with free boundary

    H. W. Alt;Luis A Caffarelli

  • The dirichlet problem for nonlinear second‐order elliptic equations I. Monge‐ampégre equation

    L. Caffarelli;L. Nirenberg;J. Spruck

  • Interior a priori estimates for solutions of fully non-linear equations

    Luis A. Caffarelli

  • Regularity theory for fully nonlinear integro‐differential equations

    Luis A Caffarelli;Luis Silvestre

  • Nonlocal minimal surfaces

    L. Caffarelli;Jean-Michel Roquejoffre;O. Savin

  • Interior $W^{2,p}$ estimates for solutions of the Monge-Ampère equation

    Luis A. Caffarelli

  • Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

    Luis A. Caffarelli;Sandro Salsa;Luis Silvestre

  • Variational problems with two phases and their free boundaries

    Hans Wilhelm Alt;Luis A. Caffarelli;Avner Friedman

  • On W1,p estimates for elliptic equations in divergence form

    Luis A. Caffarelli;I. Peral

  • The regularity of free boundaries in higher dimensions

    Luis A. Caffarelli

  • The Obstacle Problem Revisited.

    L. A. Caffarelli

  • The regularity of mappings with a convex potential

    Luis A. Caffarelli

  • A Geometric Approach to Free Boundary Problems

    Luis Caffarelli;Sandro Salsa

Frequent Co-Authors

Avner Friedman
Avner Friedman The Ohio State University
Luis Silvestre
Luis Silvestre University of Chicago
Louis Nirenberg
Louis Nirenberg Courant Institute of Mathematical Sciences
Enrico Valdinoci
Enrico Valdinoci University of Western Australia
Juan Luis Vázquez
Juan Luis Vázquez Autonomous University of Madrid
Joel Spruck
Joel Spruck Johns Hopkins University
Alexis F. Vasseur
Alexis F. Vasseur The University of Texas at Austin
YanYan Li
YanYan Li Rutgers, The State University of New Jersey
Jean-Michel Roquejoffre
Jean-Michel Roquejoffre Toulouse Mathematics Institute

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