Abstract

This paper raises the question of the stability of the full spectrum of an elliptic operator in divergence form (with homogeneous Dirichlet boundary conditions) with respect to domain perturbations which modify continuously a limited number of “small” eigenvalues. If the perturbations are semi-compact and modify the measure continuously, we prove that the stability of the first eigenvalue implies the stability of the full spectrum, under the hypothesis that the perturbed domain is connected.

Author information

Contact details are reproduced from the original publication and may be historical.

Dorin Bucur

Equipe de Mathématiques UMR-CNRS 6623, Université de Franche-Comté, 16, route de Gray, 25030 Besançon, France.

Jean-Paul Zolésio

CNRS-INLN, 1361 Route des Lucioles, and Centre de Mathématiques Appliquées, EMP, 2004 Route des Lucioles, 06902 Sophia Antipolis Cedex, France

Keywords

  • Domain perturbation
  • eigenvalue
  • elliptic operator
  • shape continuity

References

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Suggested citation

D. Bucur, J.-P. Zolésio. “Spectrum Stability of an Elliptic Operator to Domain Perturbations.” Journal of Convex Analysis 5 (1998), No. 1, 19–30. https://doi.org/10.68381/jca05-2

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Published by Heldermann Verlag, 1998. Rights now held by Banach Press.