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Electromagnetic waves in an inhomogeneous medium. (English) Zbl 0755.35134

(Author’s summary.) In this paper we consider the electromagnetic wave problem in an inhomogeneous medium. We first prove uniqueness of the solution using Rellich and Cauchy-Kowalewska theorems. Then we explicitly compute the Dirichlet-Neumann operator on the sphere, we reduce the equations to a problem on a truncted domain, and we give a variational formulation. This formulation reads as a compact perturbation of a coercive operator, which leads to the existence of the solution according to Fredholm’s alternative.

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
35R30 Inverse problems for PDEs
78A40 Waves and radiation in optics and electromagnetic theory
47A55 Perturbation theory of linear operators
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