Transmission eigenvalue-free regions near the real axis

We consider the interior transmission problem with one complex-valued refraction index, that is, with a damping term which does not vanish on the boundary. Under the condition that all geodesics reach the boundary, for a class of strictly concave domains, we obtain a transmission eigenvalue-free region of the form ${λ \in ℂ : C_{N} {(| λ | + 1)}^{- N} \leq | Im λ | \leq C {(| λ | + 1)}^{- 1}}$ , where $N > 1$ is arbitrary. Under extra conditions on the coefficients we get a larger transmission eigenvalue-free region of the form ${λ \in ℂ : C_{N} {(| λ | + 1)}^{- N} \leq | Im λ | \leq C}$ .

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Keywords

transmission eigenvalues, interior transmission problems

Mathematical Subject Classification

Primary: 35P15

Secondary: 35P20

Milestones

Received: 25 October 2023

Revised: 3 March 2024

Accepted: 25 April 2024

Published: 16 May 2024

Authors

Georgi Vodev
Laboratoire de Mathématiques Jean Leray Université de Nantes Nantes France

Vol. 6, No. 2, 2024

Georgi Vodev

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors