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| HAL : hal-00394228, version 1 |
| DOI : 10.1080/17476931003786659 |
| Fiche détaillée |  Récupérer au format |
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| Complex Variables and Elliptic Equations: An International Journal 55, 8-10 (2010) 795-816 |
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| Divergence operator and Poincaré inequalities on arbitrary bounded domains |
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| Ricardo Duran 1Maria Amelia Muschietti 2 |
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| (08/2010) |
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| Let $\Omega$ be an arbitrary bounded domain of $\R^n$. We study the right invertibility of the divergence on $\Omega$ in weighted Lebesgue and Sobolev spaces on $\Omega$, and rely this invertibility to a geometric characterization of $\Omega$ and to weighted Poincaré inequalities on $\Omega$. We recover, in particular, well-known results on the right invertibility of the divergence in Sobolev spaces when $\Omega$ is Lipschitz or, more generally, when $\Omega$ is a John domain, and focus on the case of $s$-John domains. |
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| 1 : | Facultad de Ciencias Exactas y Naturales, Departamento de Matematica |
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University of Buenos Aires |
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| 2 : | Facultad de Ciencias Exactas, Departamento de Matematica |
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Universidad Nacional de la Plata |
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| 3 : | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00394228, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00394228 | |
| oai:hal.archives-ouvertes.fr:hal-00394228 | |
| Contributeur : Emmanuel Russ | |
| Soumis le : Jeudi 11 Juin 2009, 16:10:44 | |
| Dernière modification le : Vendredi 10 Septembre 2010, 11:46:08 | |
