On $T$-coercive interior transmission eigenvalue problems on compact manifolds with smooth boundary

Abstract

We consider an interior transmission eigenvalue problem on two compact Riemannian manifolds with common smooth boundary. We assume that this problem is locally anisotropic type. Then we prove that the set of interior transmission eigenvalues forms a discrete subset of complex plane. Moreover, we also mention the interior transmission eigenvalue free region. In order to prove our results, we employ the so-called $T$-coercivity method.