Geodesic
On the sharpneess of a certain spectral stability estimate for the Dirichlet Laplacian
Eurasian mathematical journal, Tome 1 (2010) no. 1, pp. 111-122

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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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P. D. Lamberti; M. Perin. On the sharpneess of a certain spectral stability estimate for the Dirichlet Laplacian. Eurasian mathematical journal, Tome 1 (2010) no. 1, pp. 111-122. http://geodesic.mathdoc.fr/item/EMJ_2010_1_1_a8/