Spectral Stability of Higher Order Uniformly Elliptic Operators

  • Victor Burenkov
  • Pier Domenico Lamberti
Part of the International Mathematical Series book series (IMAT, volume 9)


We prove estimates for the variation of the eigenvalues of uniformly elliptic operators with homogeneous Dirichlet or Neumann boundary conditions upon variation of the open set on which an operator is defined. We consider operators of arbitrary even order and open sets admitting arbitrary strong degeneration. The main estimate is expressed in terms of a natural and easily computable distance between open sets with continuous boundaries. Another estimate is obtained in terms of the lower Hausdorff—Pompeiu deviation of the boundaries, which in general may be much smaller than the usual Hausdorff—Pompeiu distance. Finally, in the case of diffeomorphic open sets, we obtain an estimate even without the assumption of continuity of the boundaries.


Sobolev Space Dirichlet Boundary Condition Elliptic Operator Neumann Boundary Condition Continuous Boundary 
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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Università degli Studi di PadovaItaly

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