Morrey–Sobolev Extension Domains
Abstract
We show that every uniform domain of R
n with n ≥ 2 is a Morrey-Sobolev
W 1, p-extension domain for all p ∈ [1, n), and moreover, that this result is essentially best
possible for each p ∈ [1, n) in the sense that, given a simply connected planar domain or
a domain of R
n with n ≥ 3 that is quasiconformal equivalent to a uniform domain, if it
is a W 1, p-extension domain, then it must be uniform.
Main Authors
Format
Articles
Research article
Published
2017
Series
Subjects
Publication in research information system
Publisher
Springer New York LLC
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201711294413Use this for linking
Review status
Peer reviewed
ISSN
1050-6926
DOI
https://doi.org/10.1007/s12220-016-9724-9
Language
English
Published in
Journal of Geometric Analysis
Citation
- Koskela, P., Zhang, Y., & Zhou, Y. (2017). Morrey–Sobolev Extension Domains. Journal of Geometric Analysis, 27(2), 1413-1434. https://doi.org/10.1007/s12220-016-9724-9
License
Copyright© Mathematica Josephina, Inc. 2016. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.