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| HAL : hal-00496936, version 2 |
| arXiv : 1007.0309 |
| Fiche détaillée |  Récupérer au format |
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| Proc. Edinburgh A (2012) To appear |
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| Versions disponibles : | v1 (02-07-2010) | v2 (28-01-2012) |
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| Extremal functions for Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities |
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| Jean Dolbeault 1Maria J. Esteban 1 |
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| (2012) |
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| We consider a family of Caffarelli-Kohn-Nirenberg interpolation inequalities and weighted logarithmic Hardy inequalities which have been obtained recently as a limit case of the first ones. We discuss the ranges of the parameters for which the optimal constants are achieved by extremal functions. The comparison of these optimal constants with the optimal constants of Gagliardo-Nirenberg interpolation inequalities and Gross' logarithmic Sobolev inequality, both without weights, gives a general criterion for such an existence result in some particular cases. |
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| 1 : | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Sobolev spaces – Hardy-Sobolev inequality – Caffarelli-Kohn-Nirenberg inequality – logarithmic Hardy inequality – extremal functions – Kelvin transformation – Emden-Fowler transformation – radial symmetry – symmetry breaking – existence – compactness |
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| hal-00496936, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00496936 | |
| oai:hal.archives-ouvertes.fr:hal-00496936 | |
| Contributeur : Jean Dolbeault | |
| Soumis le : Vendredi 27 Janvier 2012, 22:09:44 | |
| Dernière modification le : Samedi 28 Janvier 2012, 21:09:48 | |
