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 language | English (US) |
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Pages (from-to) | 133-178 |
Number of pages | 46 |
Journal | Acta Mathematica |
Volume | 209 |
Issue number | 1 |
DOIs | |
State | Published - Oct 2012 |
ASJC Scopus subject areas
- General Mathematics