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

Pierre-Louis Lions

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Mathematics
France
2026

D-Index & Metrics

Mathematics

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

Pierre-Louis Lions publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Pierre-Louis Lions sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 82 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 311 publications — 87th percentile

87% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Pierre-Louis Lions D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Pierre-Louis Lions sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 137 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 115 D-Index — 99th percentile

99% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

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

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