user's guide to viscosity solutions of second order partial differential equations

1992/07/01 by Michael G. Crandall, Hitoshi Ishii, Pierre-Louis Lions · 11 citations
Mathematics · #math.AP

paper · pdf

published as Bull. Amer. Math. Soc. (N.S.) 27 (1992) 1-67 · 67 pages

arxiv created 1992/07/01 · arxiv updated 2009/11/30

Abstract

The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking arguments. The range of important applications of these results is enormous. This article is a self-contained exposition of the basic theory of viscosity solutions.

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