World's Best Scientists 2026 revealed!
Pierre-Louis Lions

Pierre-Louis Lions

Award Badge
Mathematics
France
2026

D-Index & Metrics

Mathematics

D-Index
115
Citations
90195
World Ranking
21
National Ranking
3

Research.com Recognitions

  • 2026 - Research.com Mathematics in France Leader Award
  • 2025 - Research.com Mathematics in France Leader Award
  • 2023 - Research.com Mathematics in France Leader Award
  • 2008 - Fellow, The World Academy of Sciences
  • 1995 - Member of Academia Europaea
  • 1994 - Fields Medal of International Mathematical Union (IMU) ... Such nonlinear partial differential equation simply do not have smooth or even C1 solutions existing after short times. ... The only option is therefore to search for some kind of weak solution. This undertaking is in effect to figure out how to allow for certain kinds of physically correct singularities and how to forbid others. ... Lions and Crandall at last broke open the problem by focusing attention on viscosity solutions, which are defined in terms of certain inequalities holding wherever the graph of the solution is touched on one side or the other by a smooth test function.
  • 1994 - Academie des sciences, France
  • 1992 - Ampère Prize (Prix Ampère de l’Électricité de France), French Academy of Sciences

Overview

Pierre-Louis Lions is affiliated with the Collège de France in France. Their research spans several aspects of mathematics and economics, with a particular focus on applied mathematics and finance. The scientist has contributed notably to fields including nonlinear partial differential equations, stochastic processes, and economic theories and models.

Their recent papers include the following:

  • "Transport Equations and Flows with One-Sided Lipschitz Velocity Fields," 2024, Archive for Rational Mechanics and Analysis
  • "Extended mean-field games," 2020, Rendiconti Lincei Matematica e Applicazioni
  • "New regularity results for Hamilton-Jacobi equations and long time behavior of pathwise (stochastic) viscosity solutions," 2020, Research in the Mathematical Sciences

The scientist frequently publishes in a range of academic venues, including:

  • arXiv (Cornell University)
  • Journal de Mathématiques Pures et Appliquées
  • L'annuaire du Collège de France
  • Rendiconti Lincei Matematica e Applicazioni
  • Archive for Rational Mechanics and Analysis

Areas of study covered by their work include:

  • Mathematics
  • Economics, Econometrics and Finance

Subfields reflected in their publications are:

  • Applied Mathematics
  • Finance
  • Mathematical Physics
  • Economics and Econometrics
  • Modeling and Simulation

Main topics investigated in their research encompass:

  • Stochastic processes and financial applications
  • Economic theories and models
  • Nonlinear Partial Differential Equations
  • Navier-Stokes equation solutions
  • Mathematical Biology Tumor Growth
  • Random Matrices and Applications
  • Stochastic processes and statistical mechanics

Frequent co-authors with whom this scientist has collaborated extensively include:

  • Panagiotis E. Souganidis
  • Jean-Michel Lasry
  • Charles Bertucci
  • Benjamin Seeger
  • Louis Bertucci

The scientist has been recognized with several awards, including:

  • Fields Medal of International Mathematical Union (IMU), 1994
  • Academie des sciences, France, 1994
  • Ampère Prize (Prix Ampère de l'Électricité de France), French Academy of Sciences, 1992
  • Member of Academia Europaea, 1995
  • Fellow, The World Academy of Sciences, 2008

Best Publications

  • User’s guide to viscosity solutions of second order partial differential equations

    Michael G. Crandall;Hitoshi Ishii;Pierre Louis Lions

  • Viscosity solutions of Hamilton-Jacobi equations

    Michael G. Crandall;Pierre-Louis Lions

  • Nonlinear scalar field equations, I existence of a ground state

    Henri Berestycki;Henri Berestycki;Pierre-Louis Lions;Pierre-Louis Lions

  • The concentration-compactness principle in the calculus of variations. The locally compact case, part 1

    P.L. Lions

  • Ordinary differential equations, transport theory and Sobolev spaces.

    R. J. DiPerna;P. L. Lions

  • Mean Field Games

    Jean-Michel Lasry;Pierre Louis Lions;Pierre Louis Lions

  • The concentration-compactness principle in the Calculus of Variations

    Unknown

  • The Concentration-Compactness Principle in the Calculus of Variations. The limit case, Part 1

    Pierre-Louis Lions

  • Image selective smoothing and edge detection by nonlinear diffusion. II

    Luis Alvarez;Pierre-Louis Lions;Jean-Michel Morel

  • Splitting Algorithms for the Sum of Two Nonlinear Operators

    Unknown

  • Image recovery via total variation minimization and related problems

    Antonin Chambolle;Pierre-Louis Lions

  • Mathematical topics in fluid mechanics

    Pierre Louis Lions

  • Generalized Solutions of Hamilton-Jacobi Equations

    Pierre-Louis Lions

  • The concentration-compactness principle in the calculus of variations. The locally compact case, part 2

    P. L. Lions

  • Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations.

    M. G. Crandall;L. C. Evans;P. L. Lions

  • On the Cauchy problem for Boltzmann equations: global existence and weak stability

    Ronald J. DiPerna;Pierre-Louis Lions

  • The concentration-compactness principle in the calculus of variations. The locally compact case

    Pierre-Louis Lions

  • Mathematical Topics in Fluid Mechanics: Volume 2: Compressible Models

    Pierre-Louis Lions

  • Axioms and fundamental equations of image processing

    Luis Alvarez;Frédéric Guichard;Pierre Louis Lions;Jean Michel Morel

  • Orbital stability of standing waves for some nonlinear Schrödinger equations

    Thierry Cazenave;Pierre-Louis Lions

  • Stochastic differential equations with reflecting boundary conditions

    P. L. Lions;A. S. Sznitman

  • Jeux à champ moyen. I – Le cas stationnaire

    Jean-Michel Lasry;Pierre-Louis Lions;Pierre-Louis Lions

Frequent Co-Authors

Panagiotis E. Souganidis
Panagiotis E. Souganidis University of Chicago
Michael G. Crandall
Michael G. Crandall University of California, Santa Barbara
Benoît Perthame
Benoît Perthame Sorbonne University
Nader Masmoudi
Nader Masmoudi Courant Institute of Mathematical Sciences
Hitoshi Ishii
Hitoshi Ishii Waseda University
Maria J. Esteban
Maria J. Esteban Paris Dauphine University
Henri Berestycki
Henri Berestycki Centre d'Analyse et de Mathématique Sociales
Pierre Cardaliaguet
Pierre Cardaliaguet Paris Dauphine University
Lawrence C. Evans
Lawrence C. Evans University of California, Berkeley
Peter K. Friz
Peter K. Friz Technical University of Berlin

If you think any of the details on this page are incorrect, let us know.

Report an issue

We appreciate your kind effort to assist us to improve this page, it would be helpful providing us with as much detail as possible in the text box below:

Related Online Degrees & Career Pathways

For students interested in expanding their expertise beyond mathematics, exploring related fields can open new career opportunities. Business-oriented degrees such as an easiest online MBA program offer strategic and managerial skills that complement analytical mathematics knowledge, making graduates highly versatile in corporate roles.

Those aiming for leadership positions in academia or industry might consider pursuing a Doctor of Business Administration. The DBA online programs provide advanced research and practical skills while maintaining flexibility for working professionals.

Finance is another promising career pathway where mathematical skills are in high demand. Aspiring professionals can enhance their qualifications through the cheapest online masters in finance, which offers strong financial modeling and quantitative analysis training at a manageable cost.

For those eager to fast-track their education and enter the workforce sooner, exploring the fastest MBA programs online can be an excellent choice. These programs are designed for efficiency without compromising quality, helping graduates quickly enhance their career prospects.

Best Scientists Citing Pierre-Louis Lions

Trending Scientists

Recently Published Articles