Conformal spectral stability estimates for the Neumann Laplacian

V. I. Burenkov, V. Gol'dshtein, A. Ukhlov

Research output: Contribution to journalArticlepeer-review


We study the eigenvalue problem for the Neumann–Laplace operator in conformal regular planar domains Ω ⊂ C. Conformal regular domains support the Poincaré–Sobolev inequality and this allows us to estimate the variation of the eigenvalues of the Neumann Laplacian upon domain perturbation via energy type integrals. Boundaries of such domains can have any Hausdorff dimension between one and two.

Original languageAmerican English
Pages (from-to)2133-2146
Number of pages14
JournalMathematische Nachrichten
Issue number17-18
StatePublished - 1 Dec 2016


  • conformal mappings
  • eigenvalue problem
  • elliptic equations
  • quasidiscs

All Science Journal Classification (ASJC) codes

  • General Mathematics


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