Shape derivatives in Kondratiev spaces for conical diffraction

摘要

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