ELECTROMAGNETIC-WAVES IN AN INHOMOGENEOUS-MEDIUM

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 truncated 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. © 1992.