English

On the sharpness of a certain spectral stability estimate for the Dirichlet Laplacian

Spectral Theory 2010-12-24 v1 Analysis of PDEs

Abstract

We consider a spectral stability estimate by Burenkov and Lamberti concerning the variation of the eigenvalues of second order uniformly elliptic operators on variable open sets in the N-dimensional euclidean space, and we prove that it is sharp for any dimension N. This is done by studying the eigenvalue problem for the Dirichlet Laplacian on special open sets inscribed in suitable spherical cones.

Keywords

Cite

@article{arxiv.1012.5295,
  title  = {On the sharpness of a certain spectral stability estimate for the Dirichlet Laplacian},
  author = {Pier Domenico Lamberti and Marco Perin},
  journal= {arXiv preprint arXiv:1012.5295},
  year   = {2010}
}

Comments

ISSN 2077-9879. Available also at the web page http://www.enu.kz/en/emj.php