Spectral properties of the neumann-laplace operator in quasiconformal regular domains

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

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

4 Scopus citations

Abstract

In this paper we study spectral properties of the Neumann-Laplace operator in planar quasiconformal regular domains Ω ⊂ ℝ2 . This study is based on the quasiconformal theory of composition operators on Sobolev spaces. We obtain estimates of constants in Poincaré-Sobolev inequalities and as a consequence lower estimates of the first non-trivial eigenvalue of the Neumann-Laplace operator in planar quasiconformal regular domains.

Original languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages129-144
Number of pages16
DOIs
StatePublished - 1 Jan 2019

Publication series

NameContemporary Mathematics
Volume734
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Keywords

  • And phrases
  • Elliptic equations
  • Quasiconformal mappings
  • Sobolev spaces

ASJC Scopus subject areas

  • Mathematics (all)

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