Lorentz estimates for asymptotically regular fully nonlinear parabolic equations

We prove a global Lorentz estimate of the Hessian of strong solutions to the Cauchy-Dirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded $C^{1,1}$ domain. Here, we mainly assume that the associated regular nonlinearity satisfies...

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Detalles Bibliográficos
Autores: Zhang, J., Zheng, S.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2017
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/690
Acceso en línea:http://hdl.handle.net/20.500.11824/690
Access Level:acceso abierto
Palabra clave:fully nonlinear parabolic equations
asymptotically regular
strong solutions
$(\delta,R)$-vanishing condition
Lorentz spaces
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spelling Lorentz estimates for asymptotically regular fully nonlinear parabolic equationsZhang, J.Zheng, S.fully nonlinear parabolic equationsasymptotically regularstrong solutions$(\delta,R)$-vanishing conditionLorentz spacesWe prove a global Lorentz estimate of the Hessian of strong solutions to the Cauchy-Dirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded $C^{1,1}$ domain. Here, we mainly assume that the associated regular nonlinearity satisfies uniformly parabolicity and the $(\delta,R)$-vanishing condition, and the approach of constructing a regular problem by an appropriate transformation is employed.NSFC grant 11371050, NSFC-ERC grant 11611530539 and the Fundamental Research Funds for the Central Universities of China grant 2016YJS154. The second author is also supported by ERCEA Advanced Grant 2014 669689-HADE, by the MINECO project MTM2014-53850-P, by Basque Government project IT-641-13 and also by the Basque Government through the BERC 2014-2017 program and by Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323.201720172017info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/690reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Inglésinfo:eu-repo/grantAgreement/EC/H2020/669689info:eu-repo/grantAgreement/MINECO//SEV-2013-0323info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2014-2017Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/6902026-06-19T12:47:47Z
dc.title.none.fl_str_mv Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
title Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
spellingShingle Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
Zhang, J.
fully nonlinear parabolic equations
asymptotically regular
strong solutions
$(\delta,R)$-vanishing condition
Lorentz spaces
title_short Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
title_full Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
title_fullStr Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
title_full_unstemmed Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
title_sort Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
dc.creator.none.fl_str_mv Zhang, J.
Zheng, S.
author Zhang, J.
author_facet Zhang, J.
Zheng, S.
author_role author
author2 Zheng, S.
author2_role author
dc.subject.none.fl_str_mv fully nonlinear parabolic equations
asymptotically regular
strong solutions
$(\delta,R)$-vanishing condition
Lorentz spaces
topic fully nonlinear parabolic equations
asymptotically regular
strong solutions
$(\delta,R)$-vanishing condition
Lorentz spaces
description We prove a global Lorentz estimate of the Hessian of strong solutions to the Cauchy-Dirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded $C^{1,1}$ domain. Here, we mainly assume that the associated regular nonlinearity satisfies uniformly parabolicity and the $(\delta,R)$-vanishing condition, and the approach of constructing a regular problem by an appropriate transformation is employed.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017
2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/690
url http://hdl.handle.net/20.500.11824/690
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/EC/H2020/669689
info:eu-repo/grantAgreement/MINECO//SEV-2013-0323
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2014-2017
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
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repository.mail.fl_str_mv
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