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Zbl 0755.35015
Crandall, Michael G.; Ishii, Hitoshi; Lions, Pierre-Louis
User's guide to viscosity solutions of second order partial differential equations. (English)
[J] Bull. Am. Math. Soc., New Ser. 27, No.1, 1-67 (1992). ISSN 0273-0979; ISSN 1088-9485/e

Summary: The notion of viscosity solution 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.

MSC 2000:: *35D05 Existence of generalized solutions of PDE
35J60 Nonlinear elliptic equations
35K55 Nonlinear parabolic equations
35B05 General behavior of solutions of PDE
35B50 Maximum principles (PDE)
35B25 Singular perturbations (PDE)
35K65 Parabolic equations of degenerate type
35F20 General theory of first order nonlinear PDE
49L25 Viscosity solutions
35J25 Second order elliptic equations, boundary value problems
35K20 Second order parabolic equations, boundary value problems
35K15 Second order parabolic equations, initial value problems

Keywords: fully nonlinear equations; Hamilton-Jacobi equations; dynamic programming; Perron's method

Cited in: Zbl 1256.93008 Zbl 1227.32042 Zbl pre05971181 Zbl 1124.65103 Zbl 1116.35074 Zbl 1103.35033 Zbl 1056.49027 Zbl 1029.78002 Zbl 1090.35063 Zbl 1029.35079 Zbl 0978.91040 Zbl 0936.35182 Zbl 0936.35181 Zbl 0901.49026 Zbl 0884.49012 Zbl 0874.35036 Zbl 0832.35042

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