Sobolev homeomorphisms are dense in volume preserving automorphisms

Bibliographic Details
Main Author: Azevedo, Assis
Publication Date: 2019
Other Authors: Azevedo, Davide, Bessa, Mário, Torres, Maria Joana
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10400.2/13847
Summary: In this paper we prove a weak version of Lusin’s theorem for the space of Sobolev-(1,p) volume preserving homeomor- phisms on closed and connected n-dimensional manifolds, n ≥ 3, for p < n − 1. We also prove that if p > n this result is not true. More precisely, we obtain the density of Sobolev-(1,p) homeomorphisms in the space of volume pre- serving automorphisms, for the weak topology. Furthermore, the regularization of an automorphism in a uniform ball cen- tered at the identity can be done in a Sobolev-(1, p) ball with the same radius centered at the identity.
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spelling Sobolev homeomorphisms are dense in volume preserving automorphismsLusin theoremVolume preservingSobolev homeomorphismIn this paper we prove a weak version of Lusin’s theorem for the space of Sobolev-(1,p) volume preserving homeomor- phisms on closed and connected n-dimensional manifolds, n ≥ 3, for p < n − 1. We also prove that if p > n this result is not true. More precisely, we obtain the density of Sobolev-(1,p) homeomorphisms in the space of volume pre- serving automorphisms, for the weak topology. Furthermore, the regularization of an automorphism in a uniform ball cen- tered at the identity can be done in a Sobolev-(1, p) ball with the same radius centered at the identity.ElsevierRepositório AbertoAzevedo, AssisAzevedo, DavideBessa, MárioTorres, Maria Joana2023-05-25T12:02:06Z20192019-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/13847eng0022-123610.1016/j.jfa.2018.10.008info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-02-26T09:32:57Zoai:repositorioaberto.uab.pt:10400.2/13847Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T21:01:33.643567Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Sobolev homeomorphisms are dense in volume preserving automorphisms
title Sobolev homeomorphisms are dense in volume preserving automorphisms
spellingShingle Sobolev homeomorphisms are dense in volume preserving automorphisms
Azevedo, Assis
Lusin theorem
Volume preserving
Sobolev homeomorphism
title_short Sobolev homeomorphisms are dense in volume preserving automorphisms
title_full Sobolev homeomorphisms are dense in volume preserving automorphisms
title_fullStr Sobolev homeomorphisms are dense in volume preserving automorphisms
title_full_unstemmed Sobolev homeomorphisms are dense in volume preserving automorphisms
title_sort Sobolev homeomorphisms are dense in volume preserving automorphisms
author Azevedo, Assis
author_facet Azevedo, Assis
Azevedo, Davide
Bessa, Mário
Torres, Maria Joana
author_role author
author2 Azevedo, Davide
Bessa, Mário
Torres, Maria Joana
author2_role author
author
author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Azevedo, Assis
Azevedo, Davide
Bessa, Mário
Torres, Maria Joana
dc.subject.por.fl_str_mv Lusin theorem
Volume preserving
Sobolev homeomorphism
topic Lusin theorem
Volume preserving
Sobolev homeomorphism
description In this paper we prove a weak version of Lusin’s theorem for the space of Sobolev-(1,p) volume preserving homeomor- phisms on closed and connected n-dimensional manifolds, n ≥ 3, for p < n − 1. We also prove that if p > n this result is not true. More precisely, we obtain the density of Sobolev-(1,p) homeomorphisms in the space of volume pre- serving automorphisms, for the weak topology. Furthermore, the regularization of an automorphism in a uniform ball cen- tered at the identity can be done in a Sobolev-(1, p) ball with the same radius centered at the identity.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01T00:00:00Z
2023-05-25T12:02:06Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.2/13847
url http://hdl.handle.net/10400.2/13847
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-1236
10.1016/j.jfa.2018.10.008
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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