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

Pier Domenico Lamberti; Marco Perin

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arXiv · 1012.5295

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

Pier Domenico Lamberti·Marco Perin

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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.

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Pier Domenico Lamberti, Marco Perin. 2010-12-23. On the sharpness of a certain spectral stability estimate for the Dirichlet Laplacian. https://arxiv.org/abs/1012.5295

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