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

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

2010-12-22

arxiv.org/abs/1012.4961v2

Mathematics

Spectral Theory

Scientific paper

10.1007/s13163-011-0079-2

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.

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