Exterior Wedge Diffraction Problems with Dirichlet, Neumann and Impedance Boundary Conditions

Abstract

Classes of problems of wave diffraction by a plane angular screen occupying an infinite 270 degrees wedge sector are studied in a Bessel potential spaces framework. The problems are subjected to different possible combinations of boundary conditions on the faces of the wedge. Namely, under consideration there will be boundary conditions of Dirichlet-Dirichlet, Neumann-Neumann, Neumann-Dirichlet, impedance-Dirichlet, and impedance-Neumann types. Existence and uniqueness results are proved for all these cases in the weak formulation. In addition, the solutions are provided within the spaces in consideration, and higher regularity of solutions are also obtained in a scale of Bessel potential spaces.