# Transmission Eigenvalues for Elliptic Operators

@article{Hitrik2010TransmissionEF,
title={Transmission Eigenvalues for Elliptic Operators},
author={Michael Hitrik and Katsiaryna Krupchyk and Petri Ola and Lassi P{\"a}iv{\"a}rinta},
journal={SIAM J. Math. Anal.},
year={2010},
volume={43},
pages={2630-2639}
}
• Published 3 July 2010
• Mathematics
• SIAM J. Math. Anal.
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-self-adjoint 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.
46 Citations
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SIAM J. Math. Anal.
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• Mathematics
• 2010
We study the interior transmission eigenvalue problem for sign-definite multiplicative perturbations of the Laplacian in a bounded domain. We show that all but finitely many complex transmission
• Mathematics
SIAM J. Math. Anal.
• 2010
We prove the existence of an infinite discrete set of transmission eigenvalues corresponding to the scattering problem for isotropic and anisotropic inhomogeneous media for both the Helmholtz and
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It is proved the existence of an infinite discrete set of transmission eigenvalues provided that the two contrasts are of opposite signs.
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The interior transmission problem is a boundary value problem that plays a basic role in inverse scattering theory but unfortunately does not seem to be included in any existing theory in partial
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