Bilinear forms on non-homogeneous Sobolev spaces
In this paper we show that if $b\in L^2(\R^n)$, then the bilinear form defined on the product of the non-homogeneous Sobolev spaces $H_s^2(\R^n)\times H_s^2(\R^n)$, $0<s<1$ by $$ (f,g)\in H_s^2(\R^n)\times H_s^2(\R^n) \to \int_{\R^n} (Id-\Delta)^{s/2}(fg)({\bf x}) b({\bf x})d{\bf x}, $$ is con...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/193292 |
| Acceso en línea: | https://hdl.handle.net/2445/193292 |
| Access Level: | acceso abierto |
| Palabra clave: | Anàlisi funcional Espais de Sobolev Equacions en derivades parcials Equacions diferencials el·líptiques Functional analysis Sobolev spaces Partial differential equations Elliptic differential equations |
| id |
ES_7d210e3802ba04a72d60aa6199783d3f |
|---|---|
| oai_identifier_str |
oai:diposit.ub.edu:2445/193292 |
| network_acronym_str |
ES |
| network_name_str |
España |
| repository_id_str |
|
| spelling |
Bilinear forms on non-homogeneous Sobolev spacesCascante, Ma. Carme (Maria Carme)Ortega Aramburu, Joaquín M.Anàlisi funcionalEspais de SobolevEquacions en derivades parcialsEquacions diferencials el·líptiquesFunctional analysisSobolev spacesPartial differential equationsElliptic differential equationsIn this paper we show that if $b\in L^2(\R^n)$, then the bilinear form defined on the product of the non-homogeneous Sobolev spaces $H_s^2(\R^n)\times H_s^2(\R^n)$, $0<s<1$ by $$ (f,g)\in H_s^2(\R^n)\times H_s^2(\R^n) \to \int_{\R^n} (Id-\Delta)^{s/2}(fg)({\bf x}) b({\bf x})d{\bf x}, $$ is continuous if and only if the positive measure $|b({\bf x})|^2d{\bf x} $ is a trace measure for $H_s^2(\R^n)$.Walter de Gruyter2020info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/193292Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: https://doi.org/10.1515/forum-2019-0311Forum Mathematicum, 2020, vol. 32, num. 4, p. 995-1026https://doi.org/10.1515/forum-2019-0311(c) Walter de Gruyter, 2020info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1932922026-05-27T06:46:51Z |
| dc.title.none.fl_str_mv |
Bilinear forms on non-homogeneous Sobolev spaces |
| title |
Bilinear forms on non-homogeneous Sobolev spaces |
| spellingShingle |
Bilinear forms on non-homogeneous Sobolev spaces Cascante, Ma. Carme (Maria Carme) Anàlisi funcional Espais de Sobolev Equacions en derivades parcials Equacions diferencials el·líptiques Functional analysis Sobolev spaces Partial differential equations Elliptic differential equations |
| title_short |
Bilinear forms on non-homogeneous Sobolev spaces |
| title_full |
Bilinear forms on non-homogeneous Sobolev spaces |
| title_fullStr |
Bilinear forms on non-homogeneous Sobolev spaces |
| title_full_unstemmed |
Bilinear forms on non-homogeneous Sobolev spaces |
| title_sort |
Bilinear forms on non-homogeneous Sobolev spaces |
| dc.creator.none.fl_str_mv |
Cascante, Ma. Carme (Maria Carme) Ortega Aramburu, Joaquín M. |
| author |
Cascante, Ma. Carme (Maria Carme) |
| author_facet |
Cascante, Ma. Carme (Maria Carme) Ortega Aramburu, Joaquín M. |
| author_role |
author |
| author2 |
Ortega Aramburu, Joaquín M. |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Anàlisi funcional Espais de Sobolev Equacions en derivades parcials Equacions diferencials el·líptiques Functional analysis Sobolev spaces Partial differential equations Elliptic differential equations |
| topic |
Anàlisi funcional Espais de Sobolev Equacions en derivades parcials Equacions diferencials el·líptiques Functional analysis Sobolev spaces Partial differential equations Elliptic differential equations |
| description |
In this paper we show that if $b\in L^2(\R^n)$, then the bilinear form defined on the product of the non-homogeneous Sobolev spaces $H_s^2(\R^n)\times H_s^2(\R^n)$, $0<s<1$ by $$ (f,g)\in H_s^2(\R^n)\times H_s^2(\R^n) \to \int_{\R^n} (Id-\Delta)^{s/2}(fg)({\bf x}) b({\bf x})d{\bf x}, $$ is continuous if and only if the positive measure $|b({\bf x})|^2d{\bf x} $ is a trace measure for $H_s^2(\R^n)$. |
| publishDate |
2020 |
| dc.date.none.fl_str_mv |
2020 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/2445/193292 |
| url |
https://hdl.handle.net/2445/193292 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Reproducció del document publicat a: https://doi.org/10.1515/forum-2019-0311 Forum Mathematicum, 2020, vol. 32, num. 4, p. 995-1026 https://doi.org/10.1515/forum-2019-0311 |
| dc.rights.none.fl_str_mv |
(c) Walter de Gruyter, 2020 info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
(c) Walter de Gruyter, 2020 |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.none.fl_str_mv |
Walter de Gruyter |
| publisher.none.fl_str_mv |
Walter de Gruyter |
| dc.source.none.fl_str_mv |
Articles publicats en revistes (Matemàtiques i Informàtica) reponame:Dipòsit Digital de la UB instname:Universidad de Barcelona |
| instname_str |
Universidad de Barcelona |
| reponame_str |
Dipòsit Digital de la UB |
| collection |
Dipòsit Digital de la UB |
| repository.name.fl_str_mv |
|
| repository.mail.fl_str_mv |
|
| _version_ |
1869411641457639425 |
| score |
15,228081 |