This article is cited in 21 papers

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

V. I. Burenkov^a, P. D. Lamberti<sup>b

a</sup> 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.

MSC: 35P15, 35J40, 47A75, 47B25

Received: 10.01.2011
Accepted: 28.07.2011

Language: English

DOI: 10.1007/s13163-011-0079-2

Bibliographic databases:

• 
• 
• 
•