Weyl Type Bound on Positive Interior Transmission Eigenvalues

Abstract

This paper contains a lower bound of the Weyl type on the counting function of the positive eigenvalues of the interior transmission eigenvalue problem which justifies the existence of an infinite set of positive interior transmission eigenvalues. We consider the classical transmission problem as well as the case where the inhomogeneous medium contains an obstacle. One of the essential components of the proof is an estimate for the D-t-N operator for the Helmholtz equation for positive λ that replaces the standard parameter-elliptic estimate valid outside of the positive semi-axis.