Homogenization and boundary layer
نویسندگان
چکیده
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 ε-periodic. We show that, as ε → 0, the solutions converge in L2 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 [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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