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An analyticity result for the dependence of multiple eigenvalues and eigenspaces of the laplace operator upon perturbation of the domain

Published online by Cambridge University Press:  18 July 2002

Pier Domenico Lamberti  and
Massimo Lanza de Cristoforis
Pier Domenico Lamberti
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Belzoni 7, 35131, Padova, Italy e-mail: lamberti@math.unipd.it, mldc@math.unipd.it
Massimo Lanza de Cristoforis
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Belzoni 7, 35131, Padova, Italy e-mail: lamberti@math.unipd.it, mldc@math.unipd.it
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In this paper, we consider the dependence of the Dirichlet eigenvalues and eigenspaces of the Laplace operator upon perturbation of the domain of definition. We prove that the dependence of a certain eigenvalue and of the corresponding eigenspace is analytic on the set of perturbations that leave the multiplicity constant.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 1 , January 2002 , pp. 29 - 43
Copyright
2002 Glasgow Mathematical Journal Trust