Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Given a homeomorphism ϕ ∈ WM 1, we determine the conditions that guarantee the belonging of the inverse of ϕ in some Sobolev–Orlicz space WF 1. We also obtain necessary and sufficient conditions under which a homeomorphism of domains in a Euclidean space induces the bounded composition operator of Sobolev–Orlicz spaces defined by a special class of N-functions. Using these results, we establish requirements on a mapping under which the inverse homeomorphism also induces the bounded composition operator of another pair of Sobolev–Orlicz spaces which is defined by the first pair.

Original languageEnglish
Pages (from-to)649-662
Number of pages14
JournalSiberian Mathematical Journal
Volume58
Issue number4
DOIs
Publication statusPublished - 1 Jul 2017

Keywords

  • codistortion
  • composition operator
  • distortion
  • N-function
  • Sobolev–Orlicz space
  • FINITE DISTORTION
  • Sobolev-Orlicz space
  • DERIVATIVES
  • OPERATORS
  • QUASICONFORMAL MAPPINGS
  • EXTREMAL MAPPINGS

Fingerprint Dive into the research topics of 'Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space'. Together they form a unique fingerprint.

Cite this