On the uniqueness of the shape of a penetrable, anisotropic obstacle
This paper studies the direct and inverse scattering problem for time harmonic waves by an inhomogeneous anisotropic medium. In the first part, the direct problem is studied by a variational approach with nonlocal boundary conditions involving the Dirichlet-Neumann operator. The main tool in the proof of uniqueness of the inverse problem consists of an investigation of the corresponding interior transmission problem. The author combines a contraction argument with the Fredholm theory to show existence and uniqueness of this problem. With the help of special solutions, the technique of Kirsch and Kress leads to uniqueness of the inverse problem.
scientific article; zbMATH DE number 1437660
scientific article