Journal of Mathematical Sciences

, Volume 149, Issue 4, pp 1417–1452

Spectral stability of nonnegative self-adjoint operators

Authors

    • Cardiff School of MathematicsCardiff University
  • P. D. Lamberti
    • Dipartimento di Matematica Pura ed ApplicataUniversità degli Studi di Padova
  • M. Lanza de Cristoforis
    • Dipartimento di Matematica Pura ed ApplicataUniversità degli Studi di Padova
Article

DOI: 10.1007/s10958-008-0074-4

Cite this article as:
Burenkov, V.I., Lamberti, P.D. & Lanza de Cristoforis, M. J Math Sci (2008) 149: 1417. doi:10.1007/s10958-008-0074-4

Abstract

The survey is devoted to spectral stability problems for uniformly elliptic differential operators under the variation of the domain and to the accompanying estimates for the difference of the eigenvalues. Two approaches to the problem are discussed in detail. In the first one it is assumed that the domain is transformed by means of a transformation of a certain class, and the spectral stability with respect to this transformation is investigated. The second approach is based on the notion of a transition operator and allows direct comparison of the eigenvalues on domains which are close in that or another sense.

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© Springer Science+Business Media, Inc. 2008