HIGH-FREQUENCY APPROXIMATION OF THE INTERIOR DIRICHLET-TO-NEUMANN MAP AND APPLICATIONS TO THE TRANSMISSION EIGENVALUES

Georgi Vodev (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

We study the high-frequency behavior of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a non-empty smooth boundary. We show that far from the real axis it can be approximated by a simpler operator. We use this fact to get new results concerning the location of the transmission eigenvalues on the complex plane. In some cases we obtain optimal transmission eigenvalue-free regions.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Georgi Vodev. HIGH-FREQUENCY APPROXIMATION OF THE INTERIOR DIRICHLET-TO-NEUMANN MAP AND APPLICATIONS TO THE TRANSMISSION EIGENVALUES. 2017. ⟨hal-01434022v2⟩