Abstract
This paper deals with the homogenization of elliptic systems with Dirichlet boundary condition, when the coefficients of both the system and the boundary data are e-periodic. We show that, as e → 0, the solutions converge in L2 with a power rate in e, 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 [7]. It extends substantially previous results obtained for polygonal domains with sides of rational slopes as well as our previous paper [12] where the case of irrational slopes was considered.
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