Pierre-Louis Lions

Pierre-Louis Lions (French: [ljɔ̃ːs];[1] born 11 August 1956) is a French mathematician. He is a recipient of the 1994 Fields Medal.

Pierre-Louis Lions
Pierre-Louis Lions par Philippe Binant.jpg
Pierre-Louis Lions
Born (1956-08-11) 11 August 1956 (age 65)
Alma materÉcole normale supérieure
Pierre and Marie Curie University
Known forNonlinear partial differential equations
Mean field game theory
AwardsFields Medal (1994)
Scientific career
InstitutionsCollège de France
École Polytechnique
University of Paris-Dauphine
ThesisSur quelques classes d'équations aux dérivees partielles non linéaires et leur résolution numérique (1979)
Doctoral advisorHaïm Brezis
Doctoral studentsMaría J. Esteban
Olivier Guéant
Gilles Motet
Cédric Villani


His parents were Jacques-Louis Lions, a mathematician and at that time professor at the University of Nancy, who became President of the International Mathematical Union, and Andrée Olivier, his wife. He graduated from the École normale supérieure in 1977. Refusing to take the agrégation in Mathematics, he chose to carry out research in applied mathematics and received his doctorate from the University of Pierre and Marie Curie in 1979.[2]

Lions holds the position of Professor of Partial differential equations and their applications at the Collège de France in Paris (since 2002) as well as a position at École Polytechnique.[3][4] Since 2014, he has also been a visiting professor at the University of Chicago.[5]

In 1983, Lions and Michael G. Crandall wrote a paper Viscosity solutions of Hamilton-Jacobi equations. In the paper, they introduced the notion of viscosity solutions. The paper had a great influence on partial differential equations. He has also contributed to mean-field game theory.[4]

In 1986, Lions received the Prix Paul Doistau–Émile Blutet. He received the Fields Medal, for his work on theory of nonlinear partial differential equations, in 1994 while working at the University of Paris-Dauphine. He was the first to give a complete solution to the Boltzmann equation with proof. He was an invited professor at the Conservatoire national des arts et métiers (2000).[6] He is a doctor honoris causa of Heriot-Watt University[7] (Edinburgh), EPFL (2010),[8] Narvik University College (2014), and of the City University of Hong-Kong and is listed as an ISI highly cited researcher.[9]


  • Lions, P. L.; Lasry, J. M. (2007). "Large investor trading impacts on volatility". Annales de l'Institut Henri Poincaré C. 24 (2): 311. Bibcode:2007AIHPC..24..311L. doi:10.1016/j.anihpc.2005.12.006.
  • Lasry, J. M.; Lions, P. L. (2007). "Mean field games" (PDF). Japanese Journal of Mathematics. 2: 229–260. doi:10.1007/s11537-007-0657-8. S2CID 1963678.
  • Lasry, J. M.; Lions, P. L. (2006). "Jeux à champ moyen. II – Horizon fini et contrôle optimal". Comptes Rendus Mathématique. 343 (10): 679. doi:10.1016/j.crma.2006.09.018.
  • Lasry, J. M.; Lions, P. L. (2006). "Jeux à champ moyen. I – Le cas stationnaire". Comptes Rendus Mathématique. 343 (9): 619. doi:10.1016/j.crma.2006.09.019.
  • Pierre-Louis Lions, Equations aux dérivées partielles et applications, Cours et travaux du Collège de France, Paris, 2002-2015.


  • Lions, Pierre-Louis. Generalized solutions of Hamilton-Jacobi equations. Research Notes in Mathematics, 69. Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. iv+317 pp. ISBN 0-273-08556-5[10]
  • Lions, Pierre-Louis. Mathematical topics in fluid mechanics. Vol. 1. Incompressible models. Oxford Lecture Series in Mathematics and its Applications, 3. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1996. xiv+237 pp. ISBN 0-19-851487-5
  • Lions, Pierre-Louis. Mathematical topics in fluid mechanics. Vol. 2. Compressible models. Oxford Lecture Series in Mathematics and its Applications, 10. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1998. xiv+348 pp. ISBN 0-19-851488-3
  • Lions, Pierre-Louis. On Euler equations and statistical physics. Cattedra Galileiana. [Galileo Chair] Scuola Normale Superiore, Classe di Scienze, Pisa, 1998. vi+74 pp.
  • Catto, Isabelle; Le Bris, Claude; Lions, Pierre-Louis. The mathematical theory of thermodynamic limits: Thomas-Fermi type models. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 1998. xiv+277 pp. ISBN 0-19-850161-7
  • Cardaliaguet, Pierre; Delarue, François; Lasry, Jean-Michel; Lions, Pierre-Louis. The master equation and the convergence problem in mean field games. Annals of Mathematics Studies, 201. Princeton University Press, Princeton, NJ, 2019. x+212 pp. ISBN 978-0-691-19071-6; 978-0-691-19070-9


  1. ^ CORE Fields Medal Talk: Pierre-Louis Lions on Mean Field Games
  2. ^ "La Médaille Fields : 11 lauréats sur 44 sont issus de laboratoires français., Alain Connes" (PDF). www2.cnrs.fr. Retrieved 11 May 2010.
  3. ^ "Pierre-Louis Lions - Biographie" (in French). Collège de France. Retrieved 16 November 2020.
  4. ^ a b "Pierre-Louis Lions". University of Chicago. Retrieved 16 November 2020.
  5. ^ "Fields Medal". University of Chicago. Retrieved 16 November 2020.
  6. ^ Pierre-Louis Lions, « Analyse, modèles et simulations », Université de tous les savoirs, 4, 86-92, Éditions Odile Jacob, Paris, 2001.
  7. ^ Hoffmann, Ilire Hasani, Robert. "Academy of Europe: Lions Pierre-Louis". www.ae-info.org. Retrieved 2016-04-06.
  8. ^ Pousaz, Lionel (2010-11-10). "The "Magistrale" crowns the founder of Yahoo". Cite journal requires |journal= (help)
  9. ^ Thomson ISI, Lions, Pierre-Louis, ISI Highly Cited Researchers, archived from the original on 2006-03-04, retrieved 2009-06-20
  10. ^ Benton, Stanley H. (1983). "Book Review: Generalized solutions of Hamilton-Jacobi equations". Bulletin of the American Mathematical Society. 9 (2): 252–257. doi:10.1090/S0273-0979-1983-15174-1.

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