Extension theorems for external cusps with minimal regularity

Autores
Acosta Rodriguez, Gabriel; Ojea, Ignacio
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Sobolev functions defined on certain simple domains with an isolated sin- gular point (such as power type external cusps) can not be extended in standard, but in appropriate weighted spaces. In this article we show that this result holds for a large class of domains that generalizes external cusps, allowing minimal boundary regularity. The construction of our extension operator is based on a modification of reflection techniques originally de- veloped for dealing with uniform domains. The weight involved in the ex- tension appears as a consequence of the failure of the domain to comply with basic properties of uniform domains, and it turns out to be a quantification of that failure. We show that weighted, rather than standard spaces, can be treated with our approach for weights that are given by a monotonic function either of the distance to the boundary or of the distance to the tip of the cusp.
Fil: Acosta Rodriguez, Gabriel. 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
Fil: Ojea, Ignacio. 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
EXTENSION THEOREMS
EXTERNAL CUSP
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:11336/130092
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Extension theorems for external cusps with minimal regularityAcosta Rodriguez, GabrielOjea, IgnacioEXTENSION THEOREMSEXTERNAL CUSPWEIGHTED SOBOLEV SPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Sobolev functions defined on certain simple domains with an isolated sin- gular point (such as power type external cusps) can not be extended in standard, but in appropriate weighted spaces. In this article we show that this result holds for a large class of domains that generalizes external cusps, allowing minimal boundary regularity. The construction of our extension operator is based on a modification of reflection techniques originally de- veloped for dealing with uniform domains. The weight involved in the ex- tension appears as a consequence of the failure of the domain to comply with basic properties of uniform domains, and it turns out to be a quantification of that failure. We show that weighted, rather than standard spaces, can be treated with our approach for weights that are given by a monotonic function either of the distance to the boundary or of the distance to the tip of the cusp.Fil: Acosta Rodriguez, Gabriel. 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"; ArgentinaFil: Ojea, Ignacio. 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"; ArgentinaPacific Journal Mathematics2012-09info: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/11336/130092Acosta Rodriguez, Gabriel; Ojea, Ignacio; Extension theorems for external cusps with minimal regularity; Pacific Journal Mathematics; Pacific Journal Of Mathematics; 259; 1; 9-2012; 1-390030-87301945-5844CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://msp.org/pjm/2012/259-1/p01.xhtmlinfo:eu-repo/semantics/altIdentifier/doi/10.2140/pjm.2012.259.1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:43:57Zoai:ri.conicet.gov.ar:11336/130092instacron: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:34982025-09-03 09:43:58.203CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Extension theorems for external cusps with minimal regularity
title Extension theorems for external cusps with minimal regularity
spellingShingle Extension theorems for external cusps with minimal regularity
Acosta Rodriguez, Gabriel
EXTENSION THEOREMS
EXTERNAL CUSP
WEIGHTED SOBOLEV SPACES
title_short Extension theorems for external cusps with minimal regularity
title_full Extension theorems for external cusps with minimal regularity
title_fullStr Extension theorems for external cusps with minimal regularity
title_full_unstemmed Extension theorems for external cusps with minimal regularity
title_sort Extension theorems for external cusps with minimal regularity
dc.creator.none.fl_str_mv Acosta Rodriguez, Gabriel
Ojea, Ignacio
author Acosta Rodriguez, Gabriel
author_facet Acosta Rodriguez, Gabriel
Ojea, Ignacio
author_role author
author2 Ojea, Ignacio
author2_role author
dc.subject.none.fl_str_mv EXTENSION THEOREMS
EXTERNAL CUSP
WEIGHTED SOBOLEV SPACES
topic EXTENSION THEOREMS
EXTERNAL CUSP
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 Sobolev functions defined on certain simple domains with an isolated sin- gular point (such as power type external cusps) can not be extended in standard, but in appropriate weighted spaces. In this article we show that this result holds for a large class of domains that generalizes external cusps, allowing minimal boundary regularity. The construction of our extension operator is based on a modification of reflection techniques originally de- veloped for dealing with uniform domains. The weight involved in the ex- tension appears as a consequence of the failure of the domain to comply with basic properties of uniform domains, and it turns out to be a quantification of that failure. We show that weighted, rather than standard spaces, can be treated with our approach for weights that are given by a monotonic function either of the distance to the boundary or of the distance to the tip of the cusp.
Fil: Acosta Rodriguez, Gabriel. 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
Fil: Ojea, Ignacio. 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 Sobolev functions defined on certain simple domains with an isolated sin- gular point (such as power type external cusps) can not be extended in standard, but in appropriate weighted spaces. In this article we show that this result holds for a large class of domains that generalizes external cusps, allowing minimal boundary regularity. The construction of our extension operator is based on a modification of reflection techniques originally de- veloped for dealing with uniform domains. The weight involved in the ex- tension appears as a consequence of the failure of the domain to comply with basic properties of uniform domains, and it turns out to be a quantification of that failure. We show that weighted, rather than standard spaces, can be treated with our approach for weights that are given by a monotonic function either of the distance to the boundary or of the distance to the tip of the cusp.
publishDate 2012
dc.date.none.fl_str_mv 2012-09
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/11336/130092
Acosta Rodriguez, Gabriel; Ojea, Ignacio; Extension theorems for external cusps with minimal regularity; Pacific Journal Mathematics; Pacific Journal Of Mathematics; 259; 1; 9-2012; 1-39
0030-8730
1945-5844
CONICET Digital
CONICET
url http://hdl.handle.net/11336/130092
identifier_str_mv Acosta Rodriguez, Gabriel; Ojea, Ignacio; Extension theorems for external cusps with minimal regularity; Pacific Journal Mathematics; Pacific Journal Of Mathematics; 259; 1; 9-2012; 1-39
0030-8730
1945-5844
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://msp.org/pjm/2012/259-1/p01.xhtml
info:eu-repo/semantics/altIdentifier/doi/10.2140/pjm.2012.259.1
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 Pacific Journal Mathematics
publisher.none.fl_str_mv Pacific Journal Mathematics
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
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score 13.13397

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