Space quasiconformal composition operators with applications to Neumann eigenvalues

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

Research output: Contribution to journalArticlepeer-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
Article number78
JournalAnalysis and Mathematical Physics
Volume10
Issue number4
DOIs
Publication statusPublished - Dec 2020

Keywords

  • Elliptic equations
  • Quasiconformal mappings
  • Sobolev spaces

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics

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