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Periodic homogenisation of certain fully nonlinear partial differential equations

Published online by Cambridge University Press:  14 November 2011

Lawrence C. Evans
Lawrence C. Evans
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, U.S.A.
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Synopsis

We demonstrate how a fairly simple “perturbed test function” method establishes periodic homogenisation for certain Hamilton-Jacobi and fully nonlinear elliptic partial differential equations. The idea, following Lions, Papanicolaou and Varadhan, is to introduce (possibly nonsmooth) correctors, and to modify appropriately the theory of viscosity solutions, so as to eliminate then the effects of high-frequency oscillations in the coefficients.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 120 , Issue 3-4 , 1992 , pp. 245 - 265
Copyright
Copyright © Royal Society of Edinburgh 1992

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