Magnetic Neumann Laplacian on a domain with hole
Diana Barseghyan, Swanhild Bernstein, Baruch Schneider · arXiv (Cornell University) · 2023
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.