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| HAL : hal-00488915, version 2 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (09-06-2010) | v2 (08-07-2010) |
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| The Hö̈lder infinite Laplacian and Hö̈lder extensions |
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| Antonin Chambolle 1Erik Lindgren 1 |
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| ANR project ”MICA”, ”Mathematical modelling and numerical simulation, F-EADS - Ecole Polytechnique - INRIA” Collaboration(s) |
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| (03/06/2010) |
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| In this paper we study the limit as $p\to \infty$ of minimizers of the fractional $W^{s,p}$-norms. In particular, we prove that the limit satisfies a non-local and non-linear equation. We also prove the existence and uniqueness of solutions of the equation. Furthermore, we prove the existence of solutions in general for the corresponding inhomogeneous equation. By making strong use of the barriers in this construction, we obtain some regularity results. |
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| 1 : | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) |
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Polytechnique - X – CNRS : UMR7641 |
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| 2 : | Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS) |
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INRIA – Ecole des Ponts ParisTech |
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| CMAP, CERMICS |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Lipschitz extensions – Hölder extensions – Infinite Laplacian – Non-local and non-linear equations – Viscosity solutions |
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| hal-00488915, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00488915 | |
| oai:hal.archives-ouvertes.fr:hal-00488915 | |
| Contributeur : Erik Lindgren | |
| Soumis le : Mercredi 7 Juillet 2010, 10:02:30 | |
| Dernière modification le : Jeudi 8 Juillet 2010, 08:49:34 | |
