On conformal spectral gap estimates of the Dirichlet-Laplacian

V. Gol'dshtein, V. Pchelintsev, A. Ukhlov

Research output: Contribution to journalArticlepeer-review

Abstract

We study spectral stability estimates of the Dirichlet eigenvalues of the Laplacian in nonconvex domains Ω ⊂ ℝ2. With the help of these estimates, we obtain asymptotically sharp inequalities of ratios of eigenvalues in the framework of the Payne-Pólya-Weinberger inequalities. These estimates are equivalent to spectral gap estimates of the Dirichlet eigenvalues of the Laplacian in nonconvex domains in terms of conformal (hyperbolic) geometry.

Original languageEnglish
Pages (from-to)325-335
Number of pages11
JournalSt. Petersburg Mathematical Journal
Volume31
Issue number2
DOIs
StatePublished - 1 Jan 2020

Keywords

  • Conformal mappings
  • Elliptic equations
  • Sobolev spaces

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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