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This article is cited in 19 scientific papers (total in 19 papers)
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.
Received: 10.01.2011 Accepted: 28.07.2011
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