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

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.

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

References in corpus (1)

• Sharp spectral stability estimates via the Lebesgue measure of domains for higher order elliptic operators

Cited by in corpus (5)

• Conformal spectral stability for the Dirichlet-Laplace operator
• Spectral Stability Estimates of Dirichlet Divergence Form Elliptic Operators
• Spectral Stability Estimates of Neumann Divergence Form Elliptic Operators
• Asymptotic behavior of $u$-capacities and singular perturbations for the Dirichlet-Laplacian
• Conformal Spectral Stability Estimates for the Neumann Laplacian