Analysis & PDE Vol. 11, No. 1, 2018 (original) (raw)

Abstract
We study the high-frequency behaviour of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a nonempty 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.

Abstract

We study the high-frequency behaviour of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a nonempty 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

Dirichlet-to-Neumann map, transmission eigenvalues

Mathematical Subject Classification 2010

Primary: 35P15

Milestones

Received: 17 January 2017

Revised: 21 June 2017

Accepted: 10 August 2017

Published: 17 September 2017

Analysis & PDE Vol. 11, No. 1, 2018 (original) (raw)

Keywords

Mathematical Subject Classification 2010

Milestones

Authors