Asymptotic behavior of the solutions of a degenerating elliptic equation in a thin multidomain

Abstract

We study the behavior of the solutions u_ε of a degenerating elliptic equation in the framework of the dimension reduction problem coupled with an oscillating boundary. Under a suitable choice of the scalings on the source term and on the diffusivity coefficients, we prove that the limit problem is a nonlocal problem involving only the diffusion through the upper part of the domain.