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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{EMJ_2010_1_1_a8,
     author = {P. D. Lamberti and M. Perin},
     title = {On the sharpneess of a certain spectral stability estimate for the {Dirichlet} {Laplacian}},
     journal = {Eurasian mathematical journal},
     pages = {111--122},
     publisher = {mathdoc},
     volume = {1},
     number = {1},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2010_1_1_a8/}
}
TY  - JOUR
AU  - P. D. Lamberti
AU  - M. Perin
TI  - On the sharpneess of a certain spectral stability estimate for the Dirichlet Laplacian
JO  - Eurasian mathematical journal
PY  - 2010
SP  - 111
EP  - 122
VL  - 1
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2010_1_1_a8/
LA  - en
ID  - EMJ_2010_1_1_a8
ER  - 
%0 Journal Article
%A P. D. Lamberti
%A M. Perin
%T On the sharpneess of a certain spectral stability estimate for the Dirichlet Laplacian
%J Eurasian mathematical journal
%D 2010
%P 111-122
%V 1
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2010_1_1_a8/
%G en
%F EMJ_2010_1_1_a8
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/

[1] M. Abramowitz, I. A. Stegun, Handbook of mathematical functions, Dover Publications, Inc., New York, 1965

[2] V. I. Burenkov, P. D. Lamberti, “Spectral stability of Dirchlet second order uniformly elliptic operators”, J. Differential Equations, 244 (2008), 1712–1740 | DOI | MR | Zbl

[3] V. I. Burenkov, P. D. Lamberti, Sharp spectral stability estimates via the Lebesgue measure of domains for higher order elliptic operators, preprint, 2009 | MR

[4] J. Math. Sci. (N.Y.), 149 (2008), 1417–1452 | DOI | MR

[5] G. A. Cámera, “Some inequalities for the first eigenvalue of the Laplace–Beltrami operator”, Mathematical notes, Univ. de Los Andes, Mérida, 100 (1989), 67–82 | MR | Zbl

[6] E. B. Davies, Spectral theory and differential operators, Cambridge University Press, Cambridge, 1995 | MR | Zbl

[7] E. B. Davies, “Sharp boundary estimates for elliptic operators”, Math. Proc. Cambridge Philos. Soc., 129 (2000), 165–178 | DOI | MR | Zbl

[8] D. Jerison, C. E. Kenig, “The inhomogeneous Dirichlet problem in Lipschitz domains”, Journal of functional analysis, 130 (1995), 161–219 | DOI | MR | Zbl

[9] V. A. Kozlov, V. G. Maz'ya, J. Rossmann, Spectral problems associated with corner singularities of solutions to elliptic equations, Mathematical Surveys and Monographs, 85, American Mathematical Society, Providence, RI, 2001 | MR | Zbl