Semiclassical parametrix for the Maxwell equation and applications to the electromagnetic transmission eigenvalues
Analysis of PDEs
2021-02-18 v1 Mathematical Physics
math.MP
Abstract
We introduce an analog of the Dirichlet-to-Neumann map for the Maxwell equation in a bounded domain. We show that it can be approximated by a pseudodifferential operator on the boundary with a matrix-valued symbol and we compute the principal symbol. As a consequence, we obtain a parabolic region free of the transmission eigenvalues associated to the Maxwell equation.
Cite
@article{arxiv.2102.08662,
title = {Semiclassical parametrix for the Maxwell equation and applications to the electromagnetic transmission eigenvalues},
author = {Georgi Vodev},
journal= {arXiv preprint arXiv:2102.08662},
year = {2021}
}