A1 Journal article (refereed)
Sobolev homeomorphic extensions onto John domains (2020)

Koskela, P., Koski, A., & Onninen, J. (2020). Sobolev homeomorphic extensions onto John domains. Journal of Functional Analysis, 279(10), Article 108719. https://doi.org/10.1016/j.jfa.2020.108719

JYU authors or editors

Publication details

All authors or editorsKoskela, Pekka; Koski, Aleksis; Onninen, Jani

Journal or seriesJournal of Functional Analysis



Publication year2020


Issue number10

Article number108719

PublisherElsevier Inc.

Publication countryUnited States

Publication languageEnglish


Publication open accessNot open

Publication channel open access

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/71515

Web address of parallel published publication (pre-print)https://arxiv.org/abs/2004.09669


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.

Keywordsfunctional analysiscomplex analysis

Free keywordsSobolev homeomorphisms; Sobolev extensions; John domains; quasidisks

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Ministry reportingYes

Reporting Year2020

JUFO rating2

Last updated on 2024-22-04 at 23:09