The generalized Hölder and Morrey-Campanato Dirichlet problems for elliptic systems in the upper-half space

We prove well-posedness results for the Dirichlet problem in Rn + for homogeneous, second order, constant complex coe cient elliptic systems with boundary data in generalized H older spaces C !(Rn1;CM) and in generalized Morrey-Campanato spaces E !;p(Rn1;CM) under certain assumptions on the growth f...

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Detalles Bibliográficos
Autores: Marín, Juan José, Martell, José María, Mitrea, Marius
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/192839
Acceso en línea:http://hdl.handle.net/10261/192839
Access Level:acceso abierto
Palabra clave:Generalized H older space
Generalized Morrey-Campanato space
Dirichlet problem in the upper-half space
Second order elliptic system
Poisson kernel
Lamé system
Nontangential pointwise trace
Fatou type theorem
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spelling The generalized Hölder and Morrey-Campanato Dirichlet problems for elliptic systems in the upper-half spaceMarín, Juan JoséMartell, José MaríaMitrea, MariusGeneralized H older spaceGeneralized Morrey-Campanato spaceDirichlet problem in the upper-half spaceSecond order elliptic systemPoisson kernelLamé systemNontangential pointwise traceFatou type theoremWe prove well-posedness results for the Dirichlet problem in Rn + for homogeneous, second order, constant complex coe cient elliptic systems with boundary data in generalized H older spaces C !(Rn1;CM) and in generalized Morrey-Campanato spaces E !;p(Rn1;CM) under certain assumptions on the growth function !. We also identify a class of growth functions ! for which C !(Rn1;CM) = E !;p(Rn1;CM) and for which the aforementioned well-posedness results are equivalent, in the sense that they have the same unique solution, satisfying natural regularity properties and estimates.Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in R&D" (SEV-2015-0554)European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ ERC agreement no. 615112 HAPDEGMTSimons Foundation grant #281566Peer reviewedSpringer NatureMinisterio de Economía y Competitividad (España)European Research CouncilSimons FoundationMartell, José María [0000-0001-6788-4769]Mitrea, Marius [0000-0002-5195-5953]Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]201920192019info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Postprintinfo:eu-repo/semantics/acceptedVersionhttp://hdl.handle.net/10261/192839reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/EC/FP7/615112info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/SEV-2015-0554https://doi.org/10.1007/s11118-019-09793-9Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/1928392026-05-22T06:33:51Z
dc.title.none.fl_str_mv The generalized Hölder and Morrey-Campanato Dirichlet problems for elliptic systems in the upper-half space
title The generalized Hölder and Morrey-Campanato Dirichlet problems for elliptic systems in the upper-half space
spellingShingle The generalized Hölder and Morrey-Campanato Dirichlet problems for elliptic systems in the upper-half space
Marín, Juan José
Generalized H older space
Generalized Morrey-Campanato space
Dirichlet problem in the upper-half space
Second order elliptic system
Poisson kernel
Lamé system
Nontangential pointwise trace
Fatou type theorem
title_short The generalized Hölder and Morrey-Campanato Dirichlet problems for elliptic systems in the upper-half space
title_full The generalized Hölder and Morrey-Campanato Dirichlet problems for elliptic systems in the upper-half space
title_fullStr The generalized Hölder and Morrey-Campanato Dirichlet problems for elliptic systems in the upper-half space
title_full_unstemmed The generalized Hölder and Morrey-Campanato Dirichlet problems for elliptic systems in the upper-half space
title_sort The generalized Hölder and Morrey-Campanato Dirichlet problems for elliptic systems in the upper-half space
dc.creator.none.fl_str_mv Marín, Juan José
Martell, José María
Mitrea, Marius
author Marín, Juan José
author_facet Marín, Juan José
Martell, José María
Mitrea, Marius
author_role author
author2 Martell, José María
Mitrea, Marius
author2_role author
author
dc.contributor.none.fl_str_mv Ministerio de Economía y Competitividad (España)
European Research Council
Simons Foundation
Martell, José María [0000-0001-6788-4769]
Mitrea, Marius [0000-0002-5195-5953]
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Generalized H older space
Generalized Morrey-Campanato space
Dirichlet problem in the upper-half space
Second order elliptic system
Poisson kernel
Lamé system
Nontangential pointwise trace
Fatou type theorem
topic Generalized H older space
Generalized Morrey-Campanato space
Dirichlet problem in the upper-half space
Second order elliptic system
Poisson kernel
Lamé system
Nontangential pointwise trace
Fatou type theorem
description We prove well-posedness results for the Dirichlet problem in Rn + for homogeneous, second order, constant complex coe cient elliptic systems with boundary data in generalized H older spaces C !(Rn1;CM) and in generalized Morrey-Campanato spaces E !;p(Rn1;CM) under certain assumptions on the growth function !. We also identify a class of growth functions ! for which C !(Rn1;CM) = E !;p(Rn1;CM) and for which the aforementioned well-posedness results are equivalent, in the sense that they have the same unique solution, satisfying natural regularity properties and estimates.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019
2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Postprint
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/192839
url http://hdl.handle.net/10261/192839
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
#PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/EC/FP7/615112
info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/SEV-2015-0554
https://doi.org/10.1007/s11118-019-09793-9
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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