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arXiv · 1007.0503

Transmission eigenvalues for elliptic operators

Michael Hitrik·Katsiaryna Krupchyk·Petri Ola·Lassi Päivärinta
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Abstract

A reduction of the transmission eigenvalue problem for multiplicative sign-definite perturbations of elliptic operators with constant coefficients to an eigenvalue problem for a non-selfadjoint compact operator is given. Sufficient conditions for the existence of transmission eigenvalues and completeness of generalized eigenstates for the transmission eigenvalue problem are derived. In the trace class case, the generic existence of transmission eigenvalues is established.

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Michael Hitrik, Katsiaryna Krupchyk, Petri Ola, Lassi Päivärinta. 2010-07-03. Transmission eigenvalues for elliptic operators. https://arxiv.org/abs/1007.0503

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