Sobolev homeomorphic extensions onto John domains

Pekka Koskela, Aleksis Koski, Jani Onninen

Research output: Contribution to journalArticlepeer-review

Abstract

Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general targets, this Sobolev variant of the classical Jordan-Schöenflies theorem may admit no solution - it is possible to have a boundary homeomorphism which admits a continuous W1,2-extension but not even a homeomorphic W1,1-extension. We prove that if the target is assumed to be a John disk, then any boundary homeomorphism from the unit circle admits a Sobolev homeomorphic extension for all exponents p<2. John disks, being one sided quasidisks, are of fundamental importance in Geometric Function Theory.

Original languageEnglish (US)
Article number108719
JournalJournal of Functional Analysis
Volume279
Issue number10
DOIs
StatePublished - Dec 1 2020

Keywords

  • John domains
  • Quasidisks
  • Sobolev extensions
  • Sobolev homeomorphisms

ASJC Scopus subject areas

  • Analysis

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