The interior transmission problem is a boundary value problem in a bounded domain which arises in the inverse scattering theory for inhomogeneous media. Although simply stated, this problem is not covered by the standard theory of elliptic partial differential equation since as it stands it is neither elliptic nor self- adjoint. Of particular interest is understanding of the spectrum associated with this boundary value problem. In this talk, I will focus on the discrete property of the interior transmission eigenvalues.
