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Rev. Mat. Complut., 2012, Volume 25, Issue 2, Pages 435–457 (Mi rmc1)  

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

V. I. Burenkova, P. D. Lambertib

a Eurasian Mathematical Institute, L.N. Gumilyov Eurasian National University, Astana 010008, Kazakhstan
b Dipartimento di Matematica Pura ed Applicata, Universit degli Studi di Padova, 35121 Padova, Italy

Abstract: We prove sharp stability estimates for the variation of the eigenvalues of non-negative self-adjoint elliptic operators of arbitrary even order upon variation of the open sets on which they are defined. These estimates are expressed in terms of the Lebesgue measure of the symmetric difference of the open sets. Both Dirichlet and Neumann boundary conditions are considered.

Funding Agency Grant Number
Università di Padova
PRIN
Russian Foundation for Basic Research 09-01-00093-A
11-01-00744-A
This research was supported by the research project “Problemi di stabilità per operatori differenziali” of the University of Padova, Italy and by the research project PRIN 2008 “Aspetti geometrici delle equazioni alle derivate parziali e questioni connesse”. The first author was also supported by the grant of RFBR— Russian Foundation for Basic Research (projects 09-01-00093-A, 11-01-00744-A).


DOI: https://doi.org/10.1007/s13163-011-0079-2


Bibliographic databases:

MSC: 35P15, 35J40, 47A75, 47B25
Received: 10.01.2011
Accepted:28.07.2011
Language:

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