Anisotropic regularity for elliptic problems with Dirac measures as data

Autores
Ojea, Ignacio
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the Possion problem with singular data given by a source supported on a one dimensional curve strictly contained in a three dimensional domain. We prove regularity results for the solution on isotropic and on anisotropic weighted spaces of Kondratiev type. Our technique is based on the study of a regularized problem. This allows us to exploit the local nature of the singularity. Our results hold with very few smoothness hypotheses on the domain and on the support of the data. We also discuss some extensions of our main results, including the two dimensional case, sources supported on closed curves and on polygonals.
Fil: Ojea, Ignacio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
SINGULAR LINE
ANISOTROPY
DIRAC DELTA
SINGULAR DATA
WEIGHTED SOBOLEV SPACES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/234645
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/234645
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Anisotropic regularity for elliptic problems with Dirac measures as dataOjea, IgnacioSINGULAR LINEANISOTROPYDIRAC DELTASINGULAR DATAWEIGHTED SOBOLEV SPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the Possion problem with singular data given by a source supported on a one dimensional curve strictly contained in a three dimensional domain. We prove regularity results for the solution on isotropic and on anisotropic weighted spaces of Kondratiev type. Our technique is based on the study of a regularized problem. This allows us to exploit the local nature of the singularity. Our results hold with very few smoothness hypotheses on the domain and on the support of the data. We also discuss some extensions of our main results, including the two dimensional case, sources supported on closed curves and on polygonals.Fil: Ojea, Ignacio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaAcademic Press Inc.2024-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/234645Ojea, Ignacio; Anisotropic regularity for elliptic problems with Dirac measures as data; Academic Press Inc.; Journal of Mathematical Analysis and Applications; 535; 1; 1-2024; 1-39, 1281041096-0813CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0022247X24000258?via%3Dihubinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2024.128104info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2306.00930info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:53:19Zoai:ri.conicet.gov.ar:11336/234645instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:53:19.619CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Anisotropic regularity for elliptic problems with Dirac measures as data
title Anisotropic regularity for elliptic problems with Dirac measures as data
spellingShingle Anisotropic regularity for elliptic problems with Dirac measures as data
Ojea, Ignacio
SINGULAR LINE
ANISOTROPY
DIRAC DELTA
SINGULAR DATA
WEIGHTED SOBOLEV SPACES
title_short Anisotropic regularity for elliptic problems with Dirac measures as data
title_full Anisotropic regularity for elliptic problems with Dirac measures as data
title_fullStr Anisotropic regularity for elliptic problems with Dirac measures as data
title_full_unstemmed Anisotropic regularity for elliptic problems with Dirac measures as data
title_sort Anisotropic regularity for elliptic problems with Dirac measures as data
dc.creator.none.fl_str_mv Ojea, Ignacio
author Ojea, Ignacio
author_facet Ojea, Ignacio
author_role author
dc.subject.none.fl_str_mv SINGULAR LINE
ANISOTROPY
DIRAC DELTA
SINGULAR DATA
WEIGHTED SOBOLEV SPACES
topic SINGULAR LINE
ANISOTROPY
DIRAC DELTA
SINGULAR DATA
WEIGHTED SOBOLEV SPACES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the Possion problem with singular data given by a source supported on a one dimensional curve strictly contained in a three dimensional domain. We prove regularity results for the solution on isotropic and on anisotropic weighted spaces of Kondratiev type. Our technique is based on the study of a regularized problem. This allows us to exploit the local nature of the singularity. Our results hold with very few smoothness hypotheses on the domain and on the support of the data. We also discuss some extensions of our main results, including the two dimensional case, sources supported on closed curves and on polygonals.
Fil: Ojea, Ignacio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We study the Possion problem with singular data given by a source supported on a one dimensional curve strictly contained in a three dimensional domain. We prove regularity results for the solution on isotropic and on anisotropic weighted spaces of Kondratiev type. Our technique is based on the study of a regularized problem. This allows us to exploit the local nature of the singularity. Our results hold with very few smoothness hypotheses on the domain and on the support of the data. We also discuss some extensions of our main results, including the two dimensional case, sources supported on closed curves and on polygonals.
publishDate 2024
dc.date.none.fl_str_mv 2024-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/234645
Ojea, Ignacio; Anisotropic regularity for elliptic problems with Dirac measures as data; Academic Press Inc.; Journal of Mathematical Analysis and Applications; 535; 1; 1-2024; 1-39, 128104
1096-0813
CONICET Digital
CONICET
url http://hdl.handle.net/11336/234645
identifier_str_mv Ojea, Ignacio; Anisotropic regularity for elliptic problems with Dirac measures as data; Academic Press Inc.; Journal of Mathematical Analysis and Applications; 535; 1; 1-2024; 1-39, 128104
1096-0813
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0022247X24000258?via%3Dihub
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2024.128104
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2306.00930
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc.
publisher.none.fl_str_mv Academic Press Inc.
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1846782228334379008
score 12.982451

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