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Bulletin of the American Mathematical Society

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

Authors: Michael G. Crandall, Hitoshi Ishii and Pierre-Louis Lions
Journal: Bull. Amer. Math. Soc. 27 (1992), 1-67
MSC (2000): Primary 35J60; Secondary 35B05, 35D05, 35G20
MathSciNet review: 1118699
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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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Keywords: Viscosity solutions, partial differential equations, fully nonlinear equations, elliptic equations, parabolic equations, Hamilton-Jacobi equations, dynamic programming, nonlinear boundary value problems, generalized solutions, maximum principles, comparison theorems, Perron's method
Article copyright: © Copyright 1992 American Mathematical Society