The Spectral Analysis of the Interior Transmission Eigenvalue Problem for Maxwell's Equations
Analysis of PDEs
2021-04-05 v3
Abstract
In this paper we consider the transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that has fixed sign (only) in a neighborhood of the boundary. We study this problem in the framework of semiclassical analysis and relate the transmission eigenvalues to the spectrum of a Hilbert-Schmidt operator. Under the additional assumption that the contrast is constant in a neighborhood of the boundary, we prove that the set of transmission eigenvalues is discrete, infinite and without finite accumulation points. A notion of generalized eigenfunctions is introduced and a denseness result is obtained in an appropriate solution space.
Cite
@article{arxiv.1707.04815,
title = {The Spectral Analysis of the Interior Transmission Eigenvalue Problem for Maxwell's Equations},
author = {Houssem Haddar and Shixu Meng},
journal= {arXiv preprint arXiv:1707.04815},
year = {2021}
}