dc.contributor.author | Hencl, Stanislav | |
dc.contributor.author | Koski, Aleksis | |
dc.contributor.author | Onninen, Jani | |
dc.date.accessioned | 2024-08-28T10:25:14Z | |
dc.date.available | 2024-08-28T10:25:14Z | |
dc.date.issued | 2024 | |
dc.identifier.citation | Hencl, S., Koski, A., & Onninen, J. (2024). Sobolev homeomorphic extensions from two to three dimensions. <i>Journal of Functional Analysis</i>, <i>286</i>(9), Article 110371. <a href="https://doi.org/10.1016/j.jfa.2024.110371" target="_blank">https://doi.org/10.1016/j.jfa.2024.110371</a> | |
dc.identifier.other | CONVID_207192386 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/96799 | |
dc.description.abstract | We study the basic question of characterizing which boundary homeomorphisms of the unit sphere can be extended to a Sobolev homeomorphism of the interior in 3D space. While the planar variants of this problem are well-understood, completely new and direct ways of constructing an extension are required in 3D. We prove, among other things, that a Sobolev homeomorphism φ: R 2 onto −−→ R 2 in W1,p loc (R 2 , R 2 ) for some p ∈ [1, ∞) admits a homeomorphic extension h: R 3 onto −−→ R 3 in W1,q loc (R 3 , R 3 ) for 1 ⩽ q < 3 2 p. Such an extension result is nearly sharp, as the bound q = 3 2 p cannot be improved due to the Hölder embedding. The case q = 3 gains an additional interest as it also provides an L 1 -variant of the celebrated Beurling-Ahlfors quasiconformal extension result. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | Elsevier | |
dc.relation.ispartofseries | Journal of Functional Analysis | |
dc.rights | CC BY 4.0 | |
dc.subject.other | Sobolev homeomorphisms | |
dc.subject.other | Sobolev extensions | |
dc.subject.other | Beurling-Ahlfors extension | |
dc.title | Sobolev homeomorphic extensions from two to three dimensions | |
dc.type | research article | |
dc.identifier.urn | URN:NBN:fi:jyu-202408285684 | |
dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
dc.contributor.laitos | Department of Mathematics and Statistics | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | |
dc.description.reviewstatus | peerReviewed | |
dc.relation.issn | 0022-1236 | |
dc.relation.numberinseries | 9 | |
dc.relation.volume | 286 | |
dc.type.version | publishedVersion | |
dc.rights.copyright | © 2024 The Authors. Published by Elsevier Inc. | |
dc.rights.accesslevel | openAccess | fi |
dc.type.publication | article | |
dc.subject.yso | funktionaalianalyysi | |
dc.format.content | fulltext | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p17780 | |
dc.rights.url | https://creativecommons.org/licenses/by/4.0/ | |
dc.relation.doi | 10.1016/j.jfa.2024.110371 | |
dc.type.okm | A1 | |