On the L p-Poisson Semigroup Associated with Elliptic Systems

We study the infinitesimal generator of the Poisson semigroup in L associated with homogeneous, second-order, strongly elliptic systems with constant complex coefficients in the upper-half space, which is proved to be the Dirichlet-to-Normal mapping in this setting. Also, its domain is identified as...

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Detalhes bibliográficos
Autores: Martell, José María, Mitrea, Dorina, Mitrea, Irina, Mitrea, Marius
Tipo de documento: artigo
Estado:Versión aceptada para publicación
Data de publicação:2017
País:España
Recursos:Consejo Superior de Investigaciones Científicas (CSIC)
Repositório:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/199109
Acesso em linha:http://hdl.handle.net/10261/199109
Access Level:Acceso aberto
Palavra-chave:Poisson semigroup
Second order elliptic system
Infinitesimal generator
Graph lipschitz domain
Higher order system
Lamé system
Poisson kernel
Nontangential maximal function
Whitney arrays
Sobolev space
Dirichlet problem
Regularity problem
Dirichlet-to-Normal map
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spelling On the L p-Poisson Semigroup Associated with Elliptic SystemsMartell, José MaríaMitrea, DorinaMitrea, IrinaMitrea, MariusPoisson semigroupSecond order elliptic systemInfinitesimal generatorGraph lipschitz domainHigher order systemLamé systemPoisson kernelNontangential maximal functionWhitney arraysSobolev spaceDirichlet problemRegularity problemDirichlet-to-Normal mapWe study the infinitesimal generator of the Poisson semigroup in L associated with homogeneous, second-order, strongly elliptic systems with constant complex coefficients in the upper-half space, which is proved to be the Dirichlet-to-Normal mapping in this setting. Also, its domain is identified as the linear subspace of the L-based Sobolev space of order one on the boundary of the upper-half space consisting of functions for which the Regularity problem is solvable. Moreover, for a class of systems containing the Lamé system, as well as all second-order, scalar elliptic operators, with constant complex coefficients, the action of the infinitesimal generator is explicitly described in terms of singular integral operators whose kernels involve first-order derivatives of the canonical fundamental solution of the given system. Furthermore, arbitrary powers of the infinitesimal generator of the said Poisson semigroup are also described in terms of higher order Sobolev spaces and a higher order Regularity problem for the system in question. Finally, we indicate how our techniques may be adapted to treat the case of higher order systems in graph Lipschitz domains.The first author acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa Programme for Centres of Excellence in R&D” (SEV-2015-0554). He also acknowledges that the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ ERC agreement no. 615112 HAPDEGMT. The second author has been supported in part by a Simons Foundation grant # 426669, the third author has been supported in part by the Simons Foundation grant #318658, while the fourth author has been supported in part by the Simons Foundation grant # 281566, and by a University of Missouri Research Leave grant.Springer NatureMinisterio de Economía y Competitividad (España)Simons FoundationEuropean CommissionConsejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]2020202020172020info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Postprintinfo:eu-repo/semantics/acceptedVersionhttp://hdl.handle.net/10261/199109reponame: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-2015http://dx.doi.org/10.1007/s11118-017-9620-3Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/1991092026-05-22T06:33:51Z
dc.title.none.fl_str_mv On the L p-Poisson Semigroup Associated with Elliptic Systems
title On the L p-Poisson Semigroup Associated with Elliptic Systems
spellingShingle On the L p-Poisson Semigroup Associated with Elliptic Systems
Martell, José María
Poisson semigroup
Second order elliptic system
Infinitesimal generator
Graph lipschitz domain
Higher order system
Lamé system
Poisson kernel
Nontangential maximal function
Whitney arrays
Sobolev space
Dirichlet problem
Regularity problem
Dirichlet-to-Normal map
title_short On the L p-Poisson Semigroup Associated with Elliptic Systems
title_full On the L p-Poisson Semigroup Associated with Elliptic Systems
title_fullStr On the L p-Poisson Semigroup Associated with Elliptic Systems
title_full_unstemmed On the L p-Poisson Semigroup Associated with Elliptic Systems
title_sort On the L p-Poisson Semigroup Associated with Elliptic Systems
dc.creator.none.fl_str_mv Martell, José María
Mitrea, Dorina
Mitrea, Irina
Mitrea, Marius
author Martell, José María
author_facet Martell, José María
Mitrea, Dorina
Mitrea, Irina
Mitrea, Marius
author_role author
author2 Mitrea, Dorina
Mitrea, Irina
Mitrea, Marius
author2_role author
author
author
dc.contributor.none.fl_str_mv Ministerio de Economía y Competitividad (España)
Simons Foundation
European Commission
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Poisson semigroup
Second order elliptic system
Infinitesimal generator
Graph lipschitz domain
Higher order system
Lamé system
Poisson kernel
Nontangential maximal function
Whitney arrays
Sobolev space
Dirichlet problem
Regularity problem
Dirichlet-to-Normal map
topic Poisson semigroup
Second order elliptic system
Infinitesimal generator
Graph lipschitz domain
Higher order system
Lamé system
Poisson kernel
Nontangential maximal function
Whitney arrays
Sobolev space
Dirichlet problem
Regularity problem
Dirichlet-to-Normal map
description We study the infinitesimal generator of the Poisson semigroup in L associated with homogeneous, second-order, strongly elliptic systems with constant complex coefficients in the upper-half space, which is proved to be the Dirichlet-to-Normal mapping in this setting. Also, its domain is identified as the linear subspace of the L-based Sobolev space of order one on the boundary of the upper-half space consisting of functions for which the Regularity problem is solvable. Moreover, for a class of systems containing the Lamé system, as well as all second-order, scalar elliptic operators, with constant complex coefficients, the action of the infinitesimal generator is explicitly described in terms of singular integral operators whose kernels involve first-order derivatives of the canonical fundamental solution of the given system. Furthermore, arbitrary powers of the infinitesimal generator of the said Poisson semigroup are also described in terms of higher order Sobolev spaces and a higher order Regularity problem for the system in question. Finally, we indicate how our techniques may be adapted to treat the case of higher order systems in graph Lipschitz domains.
publishDate 2017
dc.date.none.fl_str_mv 2017
2020
2020
2020
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/10261/199109
url http://hdl.handle.net/10261/199109
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
http://dx.doi.org/10.1007/s11118-017-9620-3
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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