Approximation of W1,p Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian

Campbell, D.; Hencl, S.; Tengvall, Ville

doi:10.1016/j.aim.2018.04.017

dc.contributor.author	Campbell, D.
dc.contributor.author	Hencl, S.
dc.contributor.author	Tengvall, Ville
dc.date.accessioned	2019-04-12T05:02:15Z
dc.date.available	2020-06-21T21:35:13Z
dc.date.issued	2018
dc.identifier.citation	Campbell, D., Hencl, S., & Tengvall, V. (2018). Approximation of W1,p Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian. <i>Advances in Mathematics</i>, <i>331</i>, 748-829. <a href="https://doi.org/10.1016/j.aim.2018.04.017" target="_blank">https://doi.org/10.1016/j.aim.2018.04.017</a>
dc.identifier.other	CONVID_28081817
dc.identifier.other	TUTKAID_77792
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/63466
dc.description.abstract	Let Ω ⊂ R n, n ≥ 4, be a domain and 1 ≤ p < [n/2], where [a] stands for the integer part of a. We construct a homeomorphism f ∈ W1,p((−1, 1)n, R n) such that Jf = det Df > 0 on a set of positive measure and Jf < 0 on a set of positive measure. It follows that there are no diffeomorphisms (or piecewise affine homeomorphisms) fk such that fk → f in W1,p .	fi
dc.format.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	Elsevier Inc.
dc.relation.ispartofseries	Advances in Mathematics
dc.rights	CC BY-NC-ND 4.0
dc.subject.other	Jacobian
dc.subject.other	Sobolev homeomorphism
dc.title	Approximation of W1,p Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian
dc.type	article
dc.identifier.urn	URN:NBN:fi:jyu-201904052076
dc.contributor.laitos	Matematiikan ja tilastotieteen laitos	fi
dc.contributor.laitos	Department of Mathematics and Statistics	en
dc.contributor.oppiaine	Matematiikka	fi
dc.contributor.oppiaine	Mathematics	en
dc.type.uri	http://purl.org/eprint/type/JournalArticle
dc.date.updated	2019-04-05T06:15:11Z
jyx.note.uri	http://urn.fi/URN:NBN:fi:jyu-201611184661
dc.type.coar	http://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatus	peerReviewed
dc.format.pagerange	748-829
dc.relation.issn	0001-8708
dc.relation.numberinseries	0
dc.relation.volume	331
dc.type.version	acceptedVersion
dc.rights.copyright	© 2018 Elsevier Inc.
dc.rights.accesslevel	openAccess	fi
dc.relation.grantnumber	277923
dc.subject.yso	approksimointi
dc.format.content	fulltext
jyx.subject.uri	http://www.yso.fi/onto/yso/p4982
dc.rights.url	https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi	10.1016/j.aim.2018.04.017
dc.relation.funder	Suomen Akatemia	fi
dc.relation.funder	Research Council of Finland	en
jyx.fundingprogram	Akatemiahanke, SA	fi
jyx.fundingprogram	Academy Project, AoF	en
jyx.fundinginformation	All authors were supported by the ERC CZ grant LL1203 of the Czech Ministry of Education. V. Tengvall was also supported by the Vilho, Yrjö and Kalle Väisälä foundation and the Academy of Finland Project 277923.
dc.type.okm	A1