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| HAL : hal-00090987, version 1 |
| arXiv : math.AP/0609101 |
| Fiche détaillée |  Récupérer au format |
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| Weighted Sobolev spaces and regularity for polyhedral domains |
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| Bernd Ammann 1Victor Nistor 2 |
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| (04/09/2006) |
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| We prove a regularity result for the Poisson problem $-\Delta u = f$, $u \vert_{\pa \PP} = g$ on a polyhedral domain $\PP \subset \RR^3$ using the \BK\ spaces $\Kond{m}{a}(\PP)$. These are weighted Sobolev spaces in which the weight is given by the distance to the set of edges \cite{Babu70, Kondratiev67}. In particular, we show that there is no loss of $\Kond{m}{a}$--regularity for solutions of strongly elliptic systems with smooth coefficients. We also establish a ``trace theorem'' for the restriction to the boundary of the functions in $\Kond{m}{a}(\PP)$. |
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| 1 : | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| 2 : | Pennsylvania State University Math Department (PENN STATE UNIVERSITY) |
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Pennsylvania State University |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| non-smooth boundary – regularity |
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| hal-00090987, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00090987 | |
| oai:hal.archives-ouvertes.fr:hal-00090987 | |
| Contributeur : Bernd Ammann | |
| Soumis le : Lundi 4 Septembre 2006, 16:29:19 | |
| Dernière modification le : Mardi 10 Avril 2007, 11:23:34 | |
