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A localized perturbation which splits the spectrum of the Laplacian

by A. Dabrowski

(Report number 2017-34)

Abstract
For any Lipschitz domain we construct an arbitrarily small, localized perturbation which splits the spectrum of the Laplacian into simple eigenvalues. We use for this purpose a Hadamard's formula and spectral stability results.

Keywords: Laplacian eigenvalue, eigenvalue perturbation, simple eigenvalue, eigenvalue multiplicity, Hadamard formula.

@Techreport{D17_730,
  author = {A. Dabrowski},
  title = {A localized perturbation which splits the spectrum of the Laplacian},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2017-34},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2017/2017-34.pdf },
  year = {2017}
}

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