Pierre-Louis Lions
Encyclopedia
Pierre-Louis Lions is a French
French people
The French are a nation that share a common French culture and speak the French language as a mother tongue. Historically, the French population are descended from peoples of Celtic, Latin and Germanic origin, and are today a mixture of several ethnic groups...

 mathematician. His parents were Jacques-Louis Lions
Jacques-Louis Lions
Jacques-Louis Lions ForMemRS was a French mathematician who made contributions to the theory of partial differential equations and to stochastic control, among other areas. He received the SIAM's John Von Neumann prize in 1986. Lions is listed as an ISI highly cited researcher.-Biography:After...

, a mathematician and at that time professor at the University of Nancy, who in particular became President of the International Mathematical Union
International Mathematical Union
The International Mathematical Union is an international non-governmental organisation devoted to international cooperation in the field of mathematics across the world. It is a member of the International Council for Science and supports the International Congress of Mathematicians...

, and Andrée Olivier, his wife. He graduated from the École Normale Supérieure
École Normale Supérieure
The École normale supérieure is one of the most prestigious French grandes écoles...

  in 1977 (same year as Jean-Christophe Yoccoz
Jean-Christophe Yoccoz
Jean-Christophe Yoccoz is a French mathematician. He was awarded a Fields Medal in 1994, for his work on dynamical systems.-Biography:...

). He received his doctorate from the University of Pierre and Marie Curie in 1979.

He studies the theory of nonlinear partial differential equations, and received the Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...

 for his mathematical work in 1994 while working at the University of Paris-Dauphine. Lions was the first to give a complete solution to the Boltzmann equation
Boltzmann equation
The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in rarefied gas...

 with proof. Other awards Lions received include the IBM Prize in 1987 and the Philip Morris Prize in 1991. He is a doctor honoris causa of Heriot-Watt University
Heriot-Watt University
Heriot-Watt University is a university based in Edinburgh, Scotland. The name commemorates George Heriot, the 16th century financier to King James, and James Watt, the great 18th century inventor and engineer....

 (Edinburgh
Edinburgh
Edinburgh is the capital city of Scotland, the second largest city in Scotland, and the eighth most populous in the United Kingdom. The City of Edinburgh Council governs one of Scotland's 32 local government council areas. The council area includes urban Edinburgh and a rural area...

) and of the City University of Hong-Kong
City University of Hong Kong
City University of Hong Kong is a comprehensive research university in Hong Kong. It was founded in 1984 as City Polytechnic of Hong Kong and became a fully accredited university in 1994. It has achieved fast growth in recent years and received international recognition for its academic achievements...

 and is listed as an ISI highly cited researcher
ISI highly cited researcher
ISI Highly Cited is a database of "highly cited researchers"—scientific researchers whose publications are most often cited in academic journals over the past decade, published by the Institute for Scientific Information...

.. Currently, he holds the position of Professor of Partial differential equations and their applications at the prestigious Collège de France
Collège de France
The Collège de France is a higher education and research establishment located in Paris, France, in the 5th arrondissement, or Latin Quarter, across the street from the historical campus of La Sorbonne at the intersection of Rue Saint-Jacques and Rue des Écoles...

 in Paris as well as a position at Ecole Polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...

.

In the paper "Viscosity solutions of Hamilton-Jacobi equations" (1983), written with Michael Crandall, he introduced the notion of viscosity solutions. This has had a great effect on the theory of partial differential equations.

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