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The asymptotic behaviour near the boundary of periodic homogenization problems via two-scale convergence

Published online by Cambridge University Press:  05 February 2008

Juan Casado-Díaz
Juan Casado-Díaz
Affiliation:
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, C. Tarfia s/n 41012 Sevilla, Spain (jcasadod@us.es)
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Abstract

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The usual asymptotic expansion for the solutions of an elliptic linear problem with oscillatory periodic coefficients is known to not be accurate near the boundary. In order to obtain a better approximation it is necessary to add to this expansion a boundary-layer term. This term has been obtained by other authors in the case of a plane boundary, such that its normal is proportional to some period. We consider the case where the normal is arbitrary.špace{-8pt}

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 1 , February 2008 , pp. 33 - 66
Copyright
2008 Royal Society of Edinburgh