Elliptic problems in thin domains with highly oscillating boundaries

Abstract

We study the Laplace operator with Neumann boundary conditions in a 2-dimensional thin domain with a higly oscillating boundary. We obtain the correct limit problem for the case where the boundary is the graph of the oscillating function ϵGϵ(x) where Gϵ(x) = a(x) + b(x)g(x/ϵ) with g periodic and a and b not necessarily constant.