Morrey–Sobolev Extension Domains
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 inJournal of Geometric Analysis
© 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.