Homogenization and boundary layers

David Gérard-Varet, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

This paper deals with the homogenization of elliptic systems with a Dirichlet boundary condition, when the coefficients of both the system and the boundary data are ε-periodic. We show that, as ε → 0, the solutions converge in L 2 with a power rate in ε, and identify the homogenized limit system. Due to a boundary layer phenomenon, this homogenized system depends in a non-trivial way on the boundary. Our analysis answers a longstanding open problem, raised for instance in [6]. It substantially extends previous results obtained for polygonal domains with sides of rational slopes as well as our previous paper [14], where the case of irrational slopes was considered.

Original languageEnglish (US)
Pages (from-to)133-178
Number of pages46
JournalActa Mathematica
Volume209
Issue number1
DOIs
StatePublished - Oct 2012

ASJC Scopus subject areas

  • Mathematics(all)

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