Abstract
The interior transmission eigenvalue problem plays a basic role in the study of inverse scattering problems for an inhomogeneous medium. In this paper, we consider the electromagnetic interior transmission eigenvalue problem for an inhomogeneous medium with conductive boundary. Our main focus is to understand the associated eigenvalue problem, more specifically to prove the transmission eigenvalues form a discrete set and show that they exist by employing a variety of variational techniques under various assumptions on the index of refraction.
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