| Type de publication : |
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Preprint, Working Paper, Document sans référence, etc. |
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| Domaine : |
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Mathématiques/Equations aux dérivées partielles
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| Titre : |
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Sobolev extension property for tree-shaped domains with self-contacting fractal boundary |
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| Auteur(s) : |
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Thibaut Deheuvels ( ) 1 |
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| Laboratoire : |
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| Équipe de recherche : |
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Equations aux dérivées partielles |
| Résumé : |
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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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Langue du texte
intégral : |
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Anglais |
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| Mots Clés : |
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Self-similar domain – Fractal boundary – Sobolev extension domain – Traces – Partial differential equations |
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