Neumann Laplacian in a perturbed domain
Spectral Theory
2021-08-10 v1
Abstract
We consider a domain with a small compact set of zero Lebesgue measure of removed. Our main result concerns the spectrum of the Neumann Laplacian defined on such domain. We prove that the spectrum of the Laplacian converges in the Hausdorff distance sense to the spectrum of the Laplacian defined on the unperturbed domain.
Keywords
Cite
@article{arxiv.2108.03646,
title = {Neumann Laplacian in a perturbed domain},
author = {Diana Barseghyan and Baruch Schneider and Ly Hong Hai},
journal= {arXiv preprint arXiv:2108.03646},
year = {2021}
}