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Eurasian Mathematical Journal, 2010, Volume 1, Number 1, Pages 111–122
(Mi emj9)
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This article is cited in 8 scientific papers (total in 8 papers)
On the sharpneess of a certain spectral stability estimate for the Dirichlet Laplacian
P. D. Lamberti, M. Perin Dipartamento di Mathematica Pura ed Applicata, Università degli Studi di Padova, Padova, Italy
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 and phrases:
elliptic equations, Dirichlet boundary conditions, stability of eigenvalues, sharp estimates, domain perturbation.
Received: 10.09.2009
Citation:
P. D. Lamberti, M. Perin, “On the sharpneess of a certain spectral stability estimate for the Dirichlet Laplacian”, Eurasian Math. J., 1:1 (2010), 111–122
Linking options:
https://www.mathnet.ru/eng/emj9 https://www.mathnet.ru/eng/emj/v1/i1/p111
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Abstract page: | 671 | Full-text PDF : | 169 | References: | 80 |
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