Shape derivatives in Kondratiev spaces for conical diffraction

Abstract

This paper studies conical diffraction problems with non-smooth grating structures. We prove existence, uniqueness and regularity results for solutions in weighted Sobolev spaces of Kondratiev type. An a priori estimate, which follows from these results, is then used to prove shape differentiablility of solutions. Finally, a characterization of the shape derivative as a solution of a modified transmission problem is given.