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Homogenisation of Dirichlet problems for monotone operators in varying domains

Published online by Cambridge University Press:  14 November 2011

Juan Casado-Díaz
Juan Casado-Díaz
Affiliation:
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Fac. de Matemáticas, C. Tarfía s/n, 41012 Sevilla, Spain
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Abstract

We study the asymptotic behaviour, for a sequence of varying open sets Ωn, of the solutions un of nonlinear Dirichlet problems for a monotone Leray–Lions operator. The method is based on the comparison between the gradient of un and the corrector for the p-Laplacian corresponding to the same geometry as the monotone operator. The representation of the limit problem and a corrector result are obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 3 , 1997 , pp. 457 - 478
Copyright
Copyright © Royal Society of Edinburgh 1997

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