Abstract

We consider Bloch wave decomposition to study the homogenization of periodically heterogeneous and perforate media in a bounded domain ? of ? n. Assuming that ? is the size of the periodicity of the structure and of the holes, we study the asymptotic behavior, as ? ? 0, of the solution of an elliptic boundary value problem with strongly oscillating coefficients posed in ? ? (? ? being ? minus the holes) with a homogeneous Dirichlet condition on the boundary of ? and a Neumann condition on the boundary of the holes. We first consider the case when ? is ? n and then localize the problem for a bounded domain ?. A new characterization of the homogenized coefficients is given via the Hessian at the origin of the first Bloch eigenvalue.