Space quasiconformal composition operators with applications to Neumann eigenvalues

Vladimir Gol’dshtein, Ritva Hurri-Syrjänen, Valerii Pchelintsev, Alexander Ukhlov

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

Abstract

In this article we obtain estimates of Neumann eigenvalues of p-Laplace operators in a large class of space domains satisfying quasihyperbolic boundary conditions. The suggested method is based on composition operators generated by quasiconformal mappings and their applications to Sobolev–Poincaré-inequalities. By using a sharp version of the reverse Hölder inequality we refine our estimates for quasi-balls, that is, images of balls under quasiconformal mappings of the whole space.

Original languageEnglish
Title of host publicationHarmonic Analysis and Partial Differential Equations
Subtitle of host publicationIn Honor of Vladimir Maz'ya
PublisherSpringer Nature
Pages141-160
Number of pages20
ISBN (Electronic)9783031254246
ISBN (Print)9783031254239
DOIs
StatePublished - 1 Jan 2023

Keywords

  • Elliptic equations
  • Quasiconformal mappings
  • Sobolev spaces

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy

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