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The perturbed test function method for viscosity solutions of nonlinear PDE

Published online by Cambridge University Press:  14 November 2011

Lawrence C. Evans
Lawrence C. Evans
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, U.S.A.
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Synopsis

The method of viscosity solutions for nonlinear partial differential equations (PDEs) justifies passages to limits by in effect using the maximum principle to convert to the corresponding limit problem for smooth test functions. We describe in this paper a “perturbed test function” device, which entails various modifications of the test functions by lower order correctors. Applications include homogenisation for quasilinear elliptic PDEs and approximation of quasilinear parabolic PDEs by systems of Hamilton-Jacobi equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 3-4 , 1989 , pp. 359 - 375
Copyright
Copyright © Royal Society of Edinburgh 1989

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