WIAS Preprint No. 1489, (2010)

Shape derivatives in Kondratiev spaces for conical diffraction



Authors

  • Kleemann, Norbert

2010 Mathematics Subject Classification

  • 78A45 49Q10 35B45 35B65 35B20

Keywords

  • System of Helmholtz equations, transmission problem, shape optimization, corner singularities, a priori estimate

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.

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