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A variational principle for the perturbation of repeated eigenvalues and applications

by A. Dabrowski

(Report number 2017-37)

Abstract
A variational principle for the shift of eigenvalues caused by a domain perturbation is derived for a class of operators which includes elliptic differential operators. This result allows the direct extension of asymptotic formulae from simple eigenvalues to repeated ones. Some interesting examples for the Laplacian are worked out explicitly for the following types of perturbation: excision of a small hole, local change of conductivity, small boundary deformation.

Keywords: Eigenvalue perturbation; repeated eigenvalue; elliptic differential operator; asymptotic expansion; small inclusion; shape deformation.

@Techreport{D17_733,
  author = {A. Dabrowski},
  title = {A variational principle for the perturbation of repeated eigenvalues and applications},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2017-37},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2017/2017-37.pdf },
  year = {2017}
}

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