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On the uniqueness of the shape of a penetrable, anisotropic obstacle. (English) Zbl 0978.35098
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.

35R30Inverse problems for PDE
35Q60PDEs in connection with optics and electromagnetic theory
78A46Inverse scattering problems