About homeomorphisms that induce composition operators on Sobolev spaces

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15 Scopus citations

Abstract

We study generalizations of the quasiconformal homeomorphisms (the so-called homeomorphisms with bounded (p,q)-distortion) that induce bounded composition operators on the Sobolev spaces with the first weak derivatives. If a homeomorphism between domains of the Euclidean space ℝn has bounded (p,q)-distortion and q>n-1 then its inverse mapping has bounded (q/(q-n+1), p/(p-n+1))-distortion. In this article, we study in detail the analytical properties of these homeomorphisms in the limit case q=n-1. The study of these classes is important because of applications of mappings with bounded (p, q)-distortion to the Sobolev type embedding theorems and nonlinear elasticity problems.

Original languageEnglish
Pages (from-to)833-845
Number of pages13
JournalComplex Variables and Elliptic Equations
Volume55
Issue number8
DOIs
StatePublished - 1 Aug 2010

Keywords

  • Composition operators
  • Mappings of finite distortion
  • Sobolev spaces

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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