User’s guide to viscosity solutions of second order partial differential equations.(English)Zbl 0755.35015

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:

 35D05 Existence of generalized solutions of PDE (MSC2000) 35J60 Nonlinear elliptic equations 35K55 Nonlinear parabolic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35B50 Maximum principles in context of PDEs 35B25 Singular perturbations in context of PDEs 35K65 Degenerate parabolic equations 35F20 Nonlinear first-order PDEs 49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games 35J25 Boundary value problems for second-order elliptic equations 35K20 Initial-boundary value problems for second-order parabolic equations 35K15 Initial value problems for second-order parabolic equations
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References:

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