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| HAL : hal-00539019, version 1 |
| arXiv : 1011.5465 |
| Fiche détaillée |  Récupérer au format |
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| The Abel Symposium 2010, Norvège (2010) |
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| About existence, symmetry and symmetry breaking for extremal functions of some interpolation functional inequalities |
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| Jean Dolbeault 1Maria J. Esteban 1 |
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| (2012) |
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| This article is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg (CKN) and weighted logarithmic Hardy (WLH) inequalities. These results have been obtained in a series of papers in collaboration with M. del Pino, S. Filippas, M. Loss, G. Tarantello and A. Tertikas. Here we put the highlights on a symmetry breaking result: extremals of some inequalities are not radially symmetric in regions where the symmetric extremals are linearly stable. Special attention is paid to the study of the critical cases for (CKN) and (WLH). |
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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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| Caffarelli-Kohn-Nirenberg inequality – Gagliardo-Nirenberg inequality – logarithmic Hardy inequality – logarithmic Sobolev inequality – extremal functions – radial symmetry – symmetry breaking – Emden-Fowler transformation – linearization – existence – compactness – optimal constants |
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| hal-00539019, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00539019 | |
| oai:hal.archives-ouvertes.fr:hal-00539019 | |
| Contributeur : Jean Dolbeault | |
| Soumis le : Mardi 23 Novembre 2010, 23:07:15 | |
| Dernière modification le : Dimanche 18 Décembre 2011, 18:14:09 | |
