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 editors: Koskela, Pekka; Koski, Aleksis; Onninen, Jani

Journal or series: Journal of Functional Analysis

ISSN: 0022-1236

eISSN: 1096-0783

Publication year: 2020

Volume: 279

Issue number: 10

Article number: 108719

Publisher: Elsevier Inc.

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1016/j.jfa.2020.108719

Publication open access: Not 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.

Keywords: functional analysis; complex analysis

Free keywords: Sobolev homeomorphisms; Sobolev extensions; John domains; quasidisks

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Related projects

Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 2