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Abstract
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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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Keywords
Dirichlet-to-Neumann map, transmission eigenvalues
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Mathematical Subject Classification 2010
Primary: 35P15
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Milestones
Received: 17 January 2017
Revised: 21 June 2017
Accepted: 10 August 2017
Published: 17 September 2017
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