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

Abstract

In this paper, we examine the interior transmission problem for Maxwell’s equations in the case where both ε and μ, the physical parameters of the scattering medium, differ from ε0 and μ0 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 ε − ε0 and μ − μ0 can change sign. We also provide results of localization and Faber–Krahn-type inequalities for the transmission eigenvalues.