Luis A Caffarelli

About

Luis A. Caffarelli is a Professor Emeritus in the Department of Mathematics at the University of Texas at Austin, holding the Sid W. Richardson Foundation Regents Chair in Mathematics #1. His research focuses on Harmonic Analysis and Partial Differential Equations, with a broad engagement in classical and modern analysis including analytic number theory, complex analysis, differential geometry, dynamical systems, functional analysis, harmonic analysis, mathematical physics, numerical analysis, probability, and stochastic processes. His work has substantial interaction and overlap with Applied Mathematics, Mathematical Biology, and Scientific Computing. Caffarelli earned his Ph.D. and M.S. from the University of Buenos Aires, Argentina, in 1972 and 1968 respectively. Throughout his distinguished career, he has received numerous prestigious awards, including the Abel Prize in 2023, the Shaw Prize in Mathematics in 2018, the Wolf Prize in Mathematics in 2013, and the Leroy P. Steele Prize for Seminal Contribution to Research in 2014, among others. He has been recognized internationally for his seminal contributions to mathematical research and has held honorary positions and memberships in various scientific academies and institutions worldwide.

Research topics

• Mathematics
• Computer Science
• Artificial Intelligence
• Pure mathematics
• Applied mathematics
• Mathematical economics
• Telecommunications
• Mathematical analysis

Selected publications

• Regularity for $$C^{1,\alpha }$$ Interface Transmission Problems

  Archive for Rational Mechanics and Analysis · 2021 · 27 citations

  1st authorCorresponding
  PublisherOA PDFDOI

• Parabolic obstacle problems. Quasi-convexity and regularity

  ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE · 2019-06-03 · 8 citations

  articleOpen access

  In a wide class of the so called Obstacle Problems of parabolic type it is shown how to improve the optimal regularity of the solution and as a consequence how to obtain space-time regularity of the corresponding free boundary.

  PublisherOA PDFDOI

• The two-phase Stefan problem with anomalous diffusion

  Advances in Mathematics · 2022-06-16 · 7 citations

  article
  PublisherDOI

• Minimal surfaces and free boundaries: Recent developments

  Bulletin of the American Mathematical Society · 2019-06-28 · 6 citations

  articleOpen access1st authorCorresponding

  Free boundaries occur in a lot of physical phenomena and are of major interest both mathematically and physically. The aim of this contribution is to describe new ideas and results developed in the last 20 years or so that deal with some nonlocal (sometimes called anomalous) free boundary problems. Actually, such free boundary problems have been known for several decades, one of the main instances being the thin obstacle problem, the so-called (scalar) Signorini free boundary problem. We will de…

  PublisherOA PDFDOI

• On a family of fully nonlinearintegrodifferential operators : from fractional Laplacian to nonlocalMonge–Ampère

  Analysis & PDE · 2024-02-05 · 4 citations

  articleOpen access1st authorCorresponding

  We introduce a new family of intermediate operators between the fractional Laplacian and the Caffarelli-Silvestre nonlocal Monge-Amp\`ere that are given by infimums of integro-differential operators. Using rearrangement techniques, we obtain representation formulas and give a connection to optimal transport. Finally, we consider a global Poisson problem, prescribing data at infinity, and prove existence, uniqueness, and $C^{1,1}$-regularity of solutions in the full space.

  PublisherOA PDFDOI

Recent grants

• On the Homogenization of some Free Boundary Problems

  NSF · $81k · 2005–2009

• Analytical and geometrical properties of non linear diffusion equations

  NSF · $625k · 2015–2022

• FRG: Collaborative Research: Emerging issues in the sciences involving non standard diffusion

  NSF · $230k · 2011–2015

Frequent coauthors

• Avner Friedman

  The Ohio State University

  70 shared

• Sandro Salsa

  Italian Institute of Technology

  27 shared

• Alessandro Torelli

  25 shared

• Hans Wilhelm Alt

  22 shared

• Ioannis Athanasopoulos

  Athens Medical Center

  21 shared

• Enrico Valdinoci

  18 shared

• Luís Silvestre

  17 shared

• Spain Lu

  Council of Science Editors

  16 shared

Awards & honors

• Abel Prize 2023
• Asociación Argentina de Mecánica Computacional (AMCA) Prize…
• The Shaw Prize in Mathematics, Hong Kong 2018
• Honorary Researcher (IMPA), Rio de Janeiro, Brazil 2016
• Elected Member Royal Spanish Academy of Sciences, Madrid 201…

Similar researchers at University of Texas at Austin

• Eric V Anslynh-92
• Boris Breizmanh-74
• Volker Brommh-74