The Born transmission eigenvalue problem. (12th September 2016) - Cakoni, Fioralba; Colton, David; Rezac, Jacob D
Abstract: In this paper we study the distribution of transmission eigenvalues in the complex plane for obstacles whose contrast is small in magnitude. We use a first order approximation of the refractive index to derive and study an approximate interior transmission problem. In the case of spherically stratified media, we prove existence and discreteness of transmission eigenvalues and derive a condition under which the complex part of transmission eigenvalues cannot lie in a strip parallel to the real axis. For obstacles with general shape, we demonstrate that if transmission eigenvalues exist then they form a discrete set.