Sobolev homeomorphic extensions onto John domains
Year of publication
2020
Authors
Koskela, Pekka; Koski, Aleksis; Onninen, Jani
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.
Show moreOrganizations and authors
Publication type
Publication format
Article
Parent publication type
Journal
Article type
Original article
Audience
ScientificPeer-reviewed
Peer-ReviewedMINEDU's publication type classification code
A1 Journal article (refereed), original researchPublication channel information
Journal
Publisher
Volume
279
Issue
10
Article number
108719
ISSN
Publication forum
Publication forum level
2
Open access
Open access in the publisher’s service
No
Self-archived
Yes
Other information
Fields of science
Mathematics
Keywords
[object Object],[object Object]
Publication country
United States
Internationality of the publisher
International
Language
English
International co-publication
Yes
Co-publication with a company
No
DOI
10.1016/j.jfa.2020.108719
The publication is included in the Ministry of Education and Culture’s Publication data collection
Yes