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Spectral stability of nonnegative self-adjoint operators

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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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Authors and Affiliations

  1. Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, UK

    V. I. Burenkov

  2. Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Via Belzoni 7, 35131, Padova, Italy

    P. D. Lamberti & M. Lanza de Cristoforis

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  1. V. I. Burenkov
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  2. P. D. Lamberti
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  3. M. Lanza de Cristoforis
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Correspondence to V. I. Burenkov.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 15, Differential and Functional Differential Equations. Part 1, 2006.

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Burenkov, V.I., Lamberti, P.D. & Lanza de Cristoforis, M. Spectral stability of nonnegative self-adjoint operators. J Math Sci 149, 1417–1452 (2008). https://doi.org/10.1007/s10958-008-0074-4

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