Bounds on positive interior transmission eigenvalues
Mathematical Physics
2015-06-05 v3 Analysis of PDEs
math.MP
Spectral Theory
Abstract
The paper contains lower bounds on the counting function of the positive eigenvalues of the interior transmission problem when the latter is elliptic. In particular, these bounds justify the existence of an infinite set of interior transmission eigenvalues and provide asymptotic estimates from above on the counting function for the large values of the wave number. They also lead to certain important upper estimates on the first few interior transmission eigenvalues. We consider the classical transmission problem as well as the case when the inhomogeneous medium contains an obstacle.
Keywords
Cite
@article{arxiv.1206.3782,
title = {Bounds on positive interior transmission eigenvalues},
author = {Evgeny Lakshtanov and Boris Vainberg},
journal= {arXiv preprint arXiv:1206.3782},
year = {2015}
}
Comments
We corrected inaccuracies cost by the wrong sign in the Green formula (17). In particular, the sign in the definition of \sigma was changed