High-frequency approximation of the interior dirichlet-to-neumann map and applications to the transmission eigenvalues
Analysis of PDEs
2017-03-29 v3 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1701.04668,
title = {High-frequency approximation of the interior dirichlet-to-neumann map and applications to the transmission eigenvalues},
author = {Georgi Vodev},
journal= {arXiv preprint arXiv:1701.04668},
year = {2017}
}