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. Analysis & PDE, 2018, 11 (1), pp.213-236. ⟨hal-01434022v3⟩