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Morrey–Sobolev Extension Domains

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Koskela, P., Zhang, Y., & Zhou, Y. (2017). Morrey–Sobolev Extension Domains. Journal of Geometric Analysis, 27 (2), 1413-1434. doi:10.1007/s12220-016-9724-9
Published in
Journal of Geometric Analysis
Authors
Koskela, Pekka |
Zhang, Yi |
Zhou, Yuan
Date
2017
Discipline
Matematiikka
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.

 
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.
Publisher
Springer New York LLC
ISSN Search the Publication Forum
1050-6926
Keywords
extensions Morrey–Sobolev space uniform domain
DOI
10.1007/s12220-016-9724-9
URI

http://urn.fi/URN:NBN:fi:jyu-201711294413

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