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Transmission eigenvalue-free regions near the real axis. II

2024/10/31 by Vodev, Georgi
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.23713

Abstract

In this paper we extend the results in [16] to more general domains. More precisely, we obtain transmission eigenvalue-free regions for the interior transmission problem with one complex-valued refraction index, that is, with a damping term which does not vanish on the boundary. In particular, we remove the non-trapping condition as well as the strict concavity condition from [16]. Instead, we impose new, more general conditions in terms of the highfrequency behavior of certain cut-off resolvents associated to exterior problems.

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