On a class of nonlocal problems with fractional gradient constraint

Bibliographic Details
Main Author: Azevedo, Assis
Publication Date: 2023
Other Authors: Rodrigues, José Francisco, Santos, Lisa
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: https://hdl.handle.net/1822/85729
Summary: We consider a Hilbertian and a charges approach to fractional gradient constraint problems of the type |D^\sigma u|\leq g, involving the distributional fractional Riesz gradient D^\sigma, 0 < \sigma < 1, extending previous results on the existence of solutions and Lagrange multipliers of these nonlocal problems. We also prove their convergence as \sigma\nearrow 1 towards their local counterparts with the gradient constraint |Du|\leq g.
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spelling On a class of nonlocal problems with fractional gradient constraintFractional gradientNonlocal variational inequalitiesGradient constraintNonlocal Lagrange multiplierElliptic quasilinear equationsCiências Naturais::MatemáticasWe consider a Hilbertian and a charges approach to fractional gradient constraint problems of the type |D^\sigma u|\leq g, involving the distributional fractional Riesz gradient D^\sigma, 0 < \sigma < 1, extending previous results on the existence of solutions and Lagrange multipliers of these nonlocal problems. We also prove their convergence as \sigma\nearrow 1 towards their local counterparts with the gradient constraint |Du|\leq g.The research of José-Francisco Rodrigues was partially done under the framework of the Project PTDC/MATPUR/28686/2017 at CMAFcIO/ULisboa. The research of Assis Azevedo and Lisa Santos was partially financed by Portuguese Funds through FCT (Fundação para a Ciência e a Tecnologia) within the Projects UIDB/00013/2020 and UIDP/00013/20EMS PressUniversidade do MinhoAzevedo, AssisRodrigues, José FranciscoSantos, Lisa20232023-01-01T00:00:00Zconference paperinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/1822/85729engEuropean Congress of Mathematics 2021978-3-98547-051-810.4171/8ECM/26978-3-98547-551-3https://ems.press/books/standalone/262info: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:RCAAP2024-05-11T05:45:28Zoai:repositorium.sdum.uminho.pt:1822/85729Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T15:28:58.753517Repositórios 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 On a class of nonlocal problems with fractional gradient constraint
title On a class of nonlocal problems with fractional gradient constraint
spellingShingle On a class of nonlocal problems with fractional gradient constraint
Azevedo, Assis
Fractional gradient
Nonlocal variational inequalities
Gradient constraint
Nonlocal Lagrange multiplier
Elliptic quasilinear equations
Ciências Naturais::Matemáticas
title_short On a class of nonlocal problems with fractional gradient constraint
title_full On a class of nonlocal problems with fractional gradient constraint
title_fullStr On a class of nonlocal problems with fractional gradient constraint
title_full_unstemmed On a class of nonlocal problems with fractional gradient constraint
title_sort On a class of nonlocal problems with fractional gradient constraint
author Azevedo, Assis
author_facet Azevedo, Assis
Rodrigues, José Francisco
Santos, Lisa
author_role author
author2 Rodrigues, José Francisco
Santos, Lisa
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Azevedo, Assis
Rodrigues, José Francisco
Santos, Lisa
dc.subject.por.fl_str_mv Fractional gradient
Nonlocal variational inequalities
Gradient constraint
Nonlocal Lagrange multiplier
Elliptic quasilinear equations
Ciências Naturais::Matemáticas
topic Fractional gradient
Nonlocal variational inequalities
Gradient constraint
Nonlocal Lagrange multiplier
Elliptic quasilinear equations
Ciências Naturais::Matemáticas
description We consider a Hilbertian and a charges approach to fractional gradient constraint problems of the type |D^\sigma u|\leq g, involving the distributional fractional Riesz gradient D^\sigma, 0 < \sigma < 1, extending previous results on the existence of solutions and Lagrange multipliers of these nonlocal problems. We also prove their convergence as \sigma\nearrow 1 towards their local counterparts with the gradient constraint |Du|\leq g.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-01-01T00:00:00Z
dc.type.driver.fl_str_mv conference paper
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/1822/85729
url https://hdl.handle.net/1822/85729
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv European Congress of Mathematics 2021
978-3-98547-051-8
10.4171/8ECM/26
978-3-98547-551-3
https://ems.press/books/standalone/262
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 EMS Press
publisher.none.fl_str_mv EMS Press
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
_version_ 1833595343669821440

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