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An integral equation approach and the interior transmission problem for Maxwell's equations
In the first part of this paper we recall the direct scattering
problem for time harmonic electromagnetic fields where arbitrary incident
fields are scattered by a medium described by a space dependent permittivity,
permeability, and conductivity. We present an integral equation approach and
recall its basic features. In the second part we investigate the corresponding
interior transmission eigenvalue problem and prove that the spectrum is
discrete. Finally, we study the inhomogeneous interior transmission problem
and show that it is uniquely solvable provided $k^2$ is not an interior
eigenvalue.