Homogenization and boundary layers

• 成果类型: Article
• 署名作者: Gerard-Varet, David; Masmoudi, Nader
• 署名单位: Universite Paris Cite; Sorbonne Universite; New York University
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-012-0083-5
• 发表日期: 2012
• 页码: 133-178
• 关键词: elliptic-systems; 2ND-ORDER; matrices; domains

摘要

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 epsilon-periodic. We show that, as epsilon -> 0, the solutions converge in L-2 with a power rate in epsilon, 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.