Magnetic Neumann Laplacian on a domain with hole
Spectral Theory
2023-01-24 v1 Analysis of PDEs
Abstract
This article gives a domain with a small compact set of removed and the magnetic Neumann Laplacian on such set. The main theorem of this article shows the description of the holes which do not change the spectrum drastically. In this article we prove that the spectrum of the magnetic Neumann Laplacian converges in the Hausdorff distance sense to the spectrum of the original operator defined on the unperturbed domain.
Keywords
Cite
@article{arxiv.2301.09181,
title = {Magnetic Neumann Laplacian on a domain with hole},
author = {Diana Barseghyan and Swanhild Bernstein and Baruch Schneider},
journal= {arXiv preprint arXiv:2301.09181},
year = {2023}
}