Transmission eigenvalues for elliptic operators
Mathematical Physics
2010-07-06 v1 math.MP
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.
Cite
@article{arxiv.1007.0503,
title = {Transmission eigenvalues for elliptic operators},
author = {Michael Hitrik and Katsiaryna Krupchyk and Petri Ola and Lassi Päivärinta},
journal= {arXiv preprint arXiv:1007.0503},
year = {2010}
}