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The Work of Pierre-Louis Lions

In: Proceedings of the International Congress of Mathematicians

Author

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  • S.R.S. Varadhan

    (New York University, Courant Institute)

Abstract

Pierre-Louis Lions has made unique contributions over the last fifteen years to mathematics. His contributions cover a variety of areas, from probability theory to partial differential equations (PDEs). Within the PDE area he has done several beautiful things in nonlinear equations. The choice of his problems has always been motivated by applications. Many of the problems in physics, engineering and economics when formulated in mathematical terms lead to nonlinear PDEs; these problems are often very hard. The nonlinearity makes each equation different. The work of Lions is important because he has developed techniques that, with variations, can be applied to classes of such problems. To say that something is nonlinear does not mean much; in fact it could even be linear. The entire class of nonlienar PDEs is therefore very extensive and one does not expect an all-inclusive theory. On the other hand, one does not want to treat each example differently and have a collection of unrelated techiques. It is thus extremely important to identify large classes that admit a unified treatment.

Suggested Citation

  • S.R.S. Varadhan, 1995. "The Work of Pierre-Louis Lions," Springer Books, in: S. D. Chatterji (ed.), Proceedings of the International Congress of Mathematicians, pages 6-10, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9078-6_2
    DOI: 10.1007/978-3-0348-9078-6_2
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