H-Index & Metrics Top Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 92 Citations 32,862 263 World Ranking 29 National Ranking 20

Research.com Recognitions

Awards & Achievements

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

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Quantum mechanics
  • Partial differential equation

Mathematical analysis, Boundary, Partial differential equation, Lipschitz continuity and Elliptic curve are his primary areas of study. His study ties his expertise on Nonlinear system together with the subject of Mathematical analysis. His studies in Boundary integrate themes in fields like Fractional Laplacian, Indicator function and Regular polygon.

His biological study spans a wide range of topics, including Moving plane, Applied mathematics and Sobolev space. His Lipschitz continuity research includes themes of Class and Monotonic function. The Elliptic curve study combines topics in areas such as Symmetry, Compact space, Invariant and Perturbation method.

His most cited work include:

  • An Extension Problem Related to the Fractional Laplacian (2212 citations)
  • Partial regularity of suitable weak solutions of the navier‐stokes equations (1252 citations)
  • Fully Nonlinear Elliptic Equations (1104 citations)

What are the main themes of his work throughout his whole career to date?

Luis A. Caffarelli mainly focuses on Mathematical analysis, Boundary, Nonlinear system, Pure mathematics and Free boundary problem. His research related to Partial differential equation, Boundary value problem, Lipschitz continuity, Differential equation and Elliptic curve might be considered part of Mathematical analysis. His Boundary study incorporates themes from Harmonic function, Class, Type and Monotonic function.

Luis A. Caffarelli has researched Nonlinear system in several fields, including Applied mathematics, Harnack's inequality and Regular polygon. His study in Bounded function extends to Pure mathematics with its themes. His Free boundary problem study integrates concerns from other disciplines, such as Stefan problem and Mixed boundary condition.

He most often published in these fields:

  • Mathematical analysis (63.93%)
  • Boundary (23.50%)
  • Nonlinear system (15.03%)

What were the highlights of his more recent work (between 2016-2021)?

  • Mathematical analysis (63.93%)
  • Boundary (23.50%)
  • Pure mathematics (13.66%)

In recent papers he was focusing on the following fields of study:

His primary areas of investigation include Mathematical analysis, Boundary, Pure mathematics, Nonlinear system and Space. The concepts of his Mathematical analysis study are interwoven with issues in Structure, Plane and Regular polygon. In the subject of general Boundary, his work in Free boundary problem and Obstacle problem is often linked to Membrane, thereby combining diverse domains of study.

His Pure mathematics research incorporates themes from Class and Uniqueness. Luis A. Caffarelli focuses mostly in the field of Nonlinear system, narrowing it down to matters related to Alpha and, in some cases, Omega, Plasma and Toroid. As a part of the same scientific study, Luis A. Caffarelli usually deals with the Harnack's inequality, concentrating on Differential equation and frequently concerns with Monge–Ampère equation.

Between 2016 and 2021, his most popular works were:

  • Obstacle problems for integro-differential operators: regularity of solutions and free boundaries (54 citations)
  • Porous medium flow with both a fractional potential pressure and fractional time derivative (35 citations)
  • On the regularity of the non-dynamic parabolic fractional obstacle problem (18 citations)

In his most recent research, the most cited papers focused on:

  • Mathematical analysis
  • Quantum mechanics
  • Geometry

His primary areas of study are Boundary, Mathematical analysis, Pure mathematics, Obstacle problem and Hölder condition. His Boundary research is multidisciplinary, incorporating perspectives in Type and Combinatorics. His research in Mathematical analysis intersects with topics in Work, Elliptic systems and Scaling.

His Pure mathematics research is multidisciplinary, incorporating elements of Minification, Euler equations, Term, Class and Bounded function. His studies deal with areas such as Characterization, Viscosity solution, Special case and Regular polygon as well as Obstacle problem. The various areas that Luis A. Caffarelli examines in his Hölder condition study include Flow, Time derivative and Mathematical physics.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Top Publications

An Extension Problem Related to the Fractional Laplacian

Luis A Caffarelli;Luis Silvestre.
Communications in Partial Differential Equations (2007)

1979 Citations

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

L. Caffarelli;R. Kohn;L. Nirenberg.
Communications on Pure and Applied Mathematics (1982)

1515 Citations

First order interpolation inequalities with weights

L. Caffarelli;R. Kohn;L. Nirenberg.
Compositio Mathematica (1984)

1060 Citations

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

Luis A. Caffarelli;Basilis Gidas;Joel Spruck.
Communications on Pure and Applied Mathematics (1989)

1058 Citations

Fully Nonlinear Elliptic Equations

Luis A. Caffarelli;Xavier Cabré.
(1995)

1036 Citations

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

L. Caffarelli;L. Nirenberg;J. Spruck.
Acta Mathematica (1985)

805 Citations

Existence and regularity for a minimum problem with free boundary

H. W. Alt;Luis A Caffarelli.
Crelle's Journal (1981)

756 Citations

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

Luis A. Caffarelli;Alexis Vasseur.
Annals of Mathematics (2010)

668 Citations

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

L. Caffarelli;L. Nirenberg;J. Spruck.
Communications on Pure and Applied Mathematics (1984)

618 Citations

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

Luis A. Caffarelli.
Annals of Mathematics (1989)

607 Citations

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking h-index is inferred from publications deemed to belong to the considered discipline.

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