Homogenization and boundary layers
David Gérard‐Varet, Nader Masmoudi · Acta Mathematica · 2012
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.