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| HAL : hal-00659241, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Sobolev extension property for tree-shaped domains with self-contacting fractal boundary |
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| Thibaut Deheuvels 1 |
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| (12/01/2012) |
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| In this paper, we investigate the existence of extension operators from $W^{1,p}(\Omega)$ to $W^{1,p}(\R^2)$ (p≥1) for a class of tree-shaped domains $\Omega$ with a self-similar fractal boundary previously studied by Mandelbrot and Frame. Such a geometry can be seen as a bidimensional modelization of the bronchial tree. When the fractal boundary has no self-contact, Jones proved that there exist such extension operators for all p≥1. In the case when the fractal boundary self-intersects, this result does not hold. Here, we prove however that extension operators exist for p |
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| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Equations aux dérivées partielles |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Self-similar domain – Fractal boundary – Sobolev extension domain – Traces – Partial differential equations |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00659241, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00659241 | |
| oai:hal.archives-ouvertes.fr:hal-00659241 | |
| Contributeur : Maryse Collin | |
| Soumis le : Jeudi 12 Janvier 2012, 13:55:51 | |
| Dernière modification le : Lundi 10 Septembre 2012, 10:16:04 | |
