Interior transmission eigenvalue problem for Maxwell's equations: The T-coercivity as an alternative approach

In this paper, we examine the interior transmission problem for Maxwells equations in the case where both and , the physical parameters of the scattering medium, differ from ₀ and ₀ modelling the background medium. Using the T-coercivity method, we propose an alternative approach to the classical techniques to prove that this problem is of Fredholm type and that the so-called transmission eigenvalues form at most a discrete set. The T-coercivity approach allows us to deal with cases where ₀ and ₀ can change sign. We also provide results of localization and FaberKrahn-type inequalities for the transmission eigenvalues.