Improved parametrix in the glancing region for the interior Dirichlet-to-Neumann map
Analysis of PDEs
2018-02-15 v2
Abstract
We study the semi-classical microlocal structure of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a non-empty smooth boundary. We build a new, improved parametrix in the glancing region compaired with that one built in [9], [12]. We also study the way in which the parametrix depends on the refraction index. As a consequence, we improve the transmission eigenvalue-free regions obtained in [12] in the isotropic case when the restrictions of the refraction indices on the boundary coincide.
Cite
@article{arxiv.1802.01857,
title = {Improved parametrix in the glancing region for the interior Dirichlet-to-Neumann map},
author = {Georgi Vodev},
journal= {arXiv preprint arXiv:1802.01857},
year = {2018}
}