Solutions of the divergence and Korn inequalities on domains with an external cusp
This paper deals with solutions of the divergence for domains with external cusps. It is known that the classic results in standard Sobolev spaces, which are basic in the variational analysis of the Stokes equations, are not valid for this class of domains. For some bounded domains Ω ⊂ Rn presenting...
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2010
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1239629X_v35_n1_p421_Duran http://hdl.handle.net/20.500.12110/paper_1239629X_v35_n1_p421_Duran |
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paper:paper_1239629X_v35_n1_p421_Duran2023-06-08T16:10:11Z Solutions of the divergence and Korn inequalities on domains with an external cusp Divergence operator Korn inequality Weighted sobolev spaces This paper deals with solutions of the divergence for domains with external cusps. It is known that the classic results in standard Sobolev spaces, which are basic in the variational analysis of the Stokes equations, are not valid for this class of domains. For some bounded domains Ω ⊂ Rn presenting power type cusps of integer dimension m ≤ n - 2, we prove the existence of solutions of the equation div u = f in weighted Sobolev spaces, where the weights are powers of the distance to the cusp. The results obtained are optimal in the sense that the powers cannot be improved. As an application, we prove existence and uniqueness of solutions of the Stokes equations in appropriate spaces for cuspidal domains. Also, we obtain weighted Korn type inequalities for this class of domains. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1239629X_v35_n1_p421_Duran http://hdl.handle.net/20.500.12110/paper_1239629X_v35_n1_p421_Duran |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Divergence operator Korn inequality Weighted sobolev spaces |
| spellingShingle |
Divergence operator Korn inequality Weighted sobolev spaces Solutions of the divergence and Korn inequalities on domains with an external cusp |
| topic_facet |
Divergence operator Korn inequality Weighted sobolev spaces |
| description |
This paper deals with solutions of the divergence for domains with external cusps. It is known that the classic results in standard Sobolev spaces, which are basic in the variational analysis of the Stokes equations, are not valid for this class of domains. For some bounded domains Ω ⊂ Rn presenting power type cusps of integer dimension m ≤ n - 2, we prove the existence of solutions of the equation div u = f in weighted Sobolev spaces, where the weights are powers of the distance to the cusp. The results obtained are optimal in the sense that the powers cannot be improved. As an application, we prove existence and uniqueness of solutions of the Stokes equations in appropriate spaces for cuspidal domains. Also, we obtain weighted Korn type inequalities for this class of domains. |
| title |
Solutions of the divergence and Korn inequalities on domains with an external cusp |
| title_short |
Solutions of the divergence and Korn inequalities on domains with an external cusp |
| title_full |
Solutions of the divergence and Korn inequalities on domains with an external cusp |
| title_fullStr |
Solutions of the divergence and Korn inequalities on domains with an external cusp |
| title_full_unstemmed |
Solutions of the divergence and Korn inequalities on domains with an external cusp |
| title_sort |
solutions of the divergence and korn inequalities on domains with an external cusp |
| publishDate |
2010 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1239629X_v35_n1_p421_Duran http://hdl.handle.net/20.500.12110/paper_1239629X_v35_n1_p421_Duran |
| _version_ |
1768546687863750656 |