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 . It substantially extends previous results obtained for polygonal domains with sides of rational slopes as well as our previous paper , where the case of irrational slopes was considered.
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