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arXiv · 1603.04604

Localization of the interior transmission eigenvalues for a ball

Vesselin Petkov·Georgi Vodev
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Abstract

We study the localization of the interior transmission eigenvalues (ITEs) in the case when the domain is the unit ball $\{x \in {\mathbb R}^d:\: |x| \leq 1\}, \: d\geq 2,$ and the coefficients $c_j(x), \: j =1,2,$ and the indices of refraction $n_j(x), \: j =1,2,$ are constants near the boundary $|x| = 1$. We prove that in this case the eigenvalue-free region obtained in [16] for strictly concave domains can be significantly improved. In particular, if $c_j(x), n_j(x), j = 1,2$ are constants for $|x| \leq 1$, we show that all (ITEs) lie in a strip $\{ \lambda \in {\mathbb C}:\:|{\rm Im}\: \lambda| \leq C\}$.

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Vesselin Petkov, Georgi Vodev. 2016-03-15. Localization of the interior transmission eigenvalues for a ball. https://arxiv.org/abs/1603.04604

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