On the asymptotic behavior of a diffraction problem with a thin layer

We investigate the behavior of the solution to an elliptic diffraction problem in the union of a smooth set Omega and a thin layer Sigma locally described by epsilon h, where h is a positive function defined on the boundary partial derivative Omega, and epsilon is the ellipticity constant of the differential operator in the thin layer Sigma. We study the problem in the limit for epsilon going to zero and prove a first-order asymptotic development by Gamma-convergence of the associated energy functional.