An explicit right inverse of the divergence operator which is continuous in weighted norms
- Autores
- Durán, Ricardo Guillermo; Muschietti, María Amelia
- Año de publicación
- 2001
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- The existence of a continuous right inverse of the divergence operator in W1,p0 (Ω)n, 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to show that the continuity also holds for some weighted norms. Our results are valid for Ω ⊂ ℝn a bounded domain which is star-shaped with respect to a ball B ⊂ Ω. The continuity results are obtained by using an explicit solution of the divergence equation and the classical theory of singular integrals of Calderón and Zygmund together with general results on weighted estimates proven by Stein. The weights considered here are of interest in the analysis of finite element methods. In particular, our result allows us to extend to the three-dimensional case the general results on uniform convergence of finite element approximations of the Stokes equations.
Facultad de Ciencias Exactas - Materia
-
Ciencias Exactas
Divergence operator
Finite elements
Singular integrals
Stokes equations
Weighted estimates - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by-nc-sa/4.0/
- Repositorio
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/83495
Ver los metadatos del registro completo
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An explicit right inverse of the divergence operator which is continuous in weighted normsDurán, Ricardo GuillermoMuschietti, María AmeliaCiencias ExactasDivergence operatorFinite elementsSingular integralsStokes equationsWeighted estimatesThe existence of a continuous right inverse of the divergence operator in W<SUP>1,p</SUP><SUB>0</SUB> (Ω)<SUP>n</SUP>, 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to show that the continuity also holds for some weighted norms. Our results are valid for Ω ⊂ ℝ<SUP>n</SUP> a bounded domain which is star-shaped with respect to a ball B ⊂ Ω. The continuity results are obtained by using an explicit solution of the divergence equation and the classical theory of singular integrals of Calderón and Zygmund together with general results on weighted estimates proven by Stein. The weights considered here are of interest in the analysis of finite element methods. In particular, our result allows us to extend to the three-dimensional case the general results on uniform convergence of finite element approximations of the Stokes equations.Facultad de Ciencias Exactas2001info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf207-219http://sedici.unlp.edu.ar/handle/10915/83495enginfo:eu-repo/semantics/altIdentifier/issn/0039-3223info:eu-repo/semantics/altIdentifier/doi/10.4064/sm148-3-2info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-17T09:58:34Zoai:sedici.unlp.edu.ar:10915/83495Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-17 09:58:34.812SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
An explicit right inverse of the divergence operator which is continuous in weighted norms |
| title |
An explicit right inverse of the divergence operator which is continuous in weighted norms |
| spellingShingle |
An explicit right inverse of the divergence operator which is continuous in weighted norms Durán, Ricardo Guillermo Ciencias Exactas Divergence operator Finite elements Singular integrals Stokes equations Weighted estimates |
| title_short |
An explicit right inverse of the divergence operator which is continuous in weighted norms |
| title_full |
An explicit right inverse of the divergence operator which is continuous in weighted norms |
| title_fullStr |
An explicit right inverse of the divergence operator which is continuous in weighted norms |
| title_full_unstemmed |
An explicit right inverse of the divergence operator which is continuous in weighted norms |
| title_sort |
An explicit right inverse of the divergence operator which is continuous in weighted norms |
| dc.creator.none.fl_str_mv |
Durán, Ricardo Guillermo Muschietti, María Amelia |
| author |
Durán, Ricardo Guillermo |
| author_facet |
Durán, Ricardo Guillermo Muschietti, María Amelia |
| author_role |
author |
| author2 |
Muschietti, María Amelia |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Ciencias Exactas Divergence operator Finite elements Singular integrals Stokes equations Weighted estimates |
| topic |
Ciencias Exactas Divergence operator Finite elements Singular integrals Stokes equations Weighted estimates |
| dc.description.none.fl_txt_mv |
The existence of a continuous right inverse of the divergence operator in W<SUP>1,p</SUP><SUB>0</SUB> (Ω)<SUP>n</SUP>, 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to show that the continuity also holds for some weighted norms. Our results are valid for Ω ⊂ ℝ<SUP>n</SUP> a bounded domain which is star-shaped with respect to a ball B ⊂ Ω. The continuity results are obtained by using an explicit solution of the divergence equation and the classical theory of singular integrals of Calderón and Zygmund together with general results on weighted estimates proven by Stein. The weights considered here are of interest in the analysis of finite element methods. In particular, our result allows us to extend to the three-dimensional case the general results on uniform convergence of finite element approximations of the Stokes equations. Facultad de Ciencias Exactas |
| description |
The existence of a continuous right inverse of the divergence operator in W<SUP>1,p</SUP><SUB>0</SUB> (Ω)<SUP>n</SUP>, 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to show that the continuity also holds for some weighted norms. Our results are valid for Ω ⊂ ℝ<SUP>n</SUP> a bounded domain which is star-shaped with respect to a ball B ⊂ Ω. The continuity results are obtained by using an explicit solution of the divergence equation and the classical theory of singular integrals of Calderón and Zygmund together with general results on weighted estimates proven by Stein. The weights considered here are of interest in the analysis of finite element methods. In particular, our result allows us to extend to the three-dimensional case the general results on uniform convergence of finite element approximations of the Stokes equations. |
| publishDate |
2001 |
| dc.date.none.fl_str_mv |
2001 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Articulo http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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http://sedici.unlp.edu.ar/handle/10915/83495 |
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http://sedici.unlp.edu.ar/handle/10915/83495 |
| dc.language.none.fl_str_mv |
eng |
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eng |
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info:eu-repo/semantics/altIdentifier/issn/0039-3223 info:eu-repo/semantics/altIdentifier/doi/10.4064/sm148-3-2 |
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info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
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openAccess |
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http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
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