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

ISSN0022-1236

eISSN1096-0783

Publication year2020

Volume279

Issue number10

Article number108719

PublisherElsevier Inc.

Publication countryUnited States

Publication languageEnglish

DOIhttps://doi.org/10.1016/j.jfa.2020.108719

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


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.


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