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2018 High-frequency approximation of the interior Dirichlet-to-Neumann map and applications to the transmission eigenvalues
Georgi Vodev
Anal. PDE 11(1): 213-236 (2018). DOI: 10.2140/apde.2018.11.213

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.

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Georgi Vodev. "High-frequency approximation of the interior Dirichlet-to-Neumann map and applications to the transmission eigenvalues." Anal. PDE 11 (1) 213 - 236, 2018. https://doi.org/10.2140/apde.2018.11.213

Information

Received: 17 January 2017; Revised: 21 June 2017; Accepted: 10 August 2017; Published: 2018
First available in Project Euclid: 20 December 2017

zbMATH: 06789264
MathSciNet: MR3707296
Digital Object Identifier: 10.2140/apde.2018.11.213

Subjects:
Primary: 35P15

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 1 • 2018
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