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 Maxwell’s equations in the case where both ε and μ, the physical parameters of the scattering medium, differ from ε 0 and μ 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 ε − ε 0 and μ − μ 0 can change sign. We also provide results of localization and Faber–Krahn-type inequalities for the transmission eigenvalues.