On $T$-coercive interior transmission eigenvalue problems on compact manifolds with smooth boundary

Naotaka Shoji

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arXiv · 1703.01743

On $T$-coercive interior transmission eigenvalue problems on compact manifolds with smooth boundary

Naotaka Shoji

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Abstract

In this paper, we consider an interior transmission eigenvalue problem on two compact Riemannian manifolds with common smooth boundary. We suppose that a couple of these manifolds is equipped with locally anisotropic type Riemannian metric tensors, i.e., these two tensors are not equivalent in a neighborhood of common boundary. Here we note that we do not assume that these manifolds are diffeomorphic. In addition, we impose some conditions of the refractive indices in a neighborhood of common boundary. Then we prove that the set of ITEs form infinite discrete set and the existence of ITE-free region. In order to prove our results, we employ so-called the $T$-coercivity method.

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BibTeX RIS

Naotaka Shoji. 2017-03-06. On $T$-coercive interior transmission eigenvalue problems on compact manifolds with smooth boundary. https://arxiv.org/abs/1703.01743

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