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
Contributing organizations
Related projects
- Geometric Analysis
- Koskela, Pekka
- Academy of Finland
- InvProbGeomPDE Inverse Problems in Partial Differential Equations and Geometry
- Salo, Mikko
- European Commission
Ministry reporting: Yes
Reporting Year: 2020
JUFO rating: 2