Portal de Periódicos da CAPES

User’s guide to viscosity solutions of second order partial differential equations

1992; American Mathematical Society; Volume: 27; Issue: 1 Linguagem: Inglês

10.1090/s0273-0979-1992-00266-5

1088-9485

Michael G. Crandall, Hitoshi Ishii, Pierre-Louis Lions,

Nonlinear Differential Equations Analysis

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.