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| HAL : hal-00595042, version 1 |
| arXiv : 1105.4511 |
| Fiche détaillée |  Récupérer au format |
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| From Poincaré to logarithmic Sobolev inequalities: a gradient flow approach |
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| Jean Dolbeault 1Bruno Nazaret 1 |
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| (23/05/2011) |
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| We use the distances introduced in a previous joint paper to exhibit the gradient flow structure of some drift-diffusion equations for a wide class of entropy functionals. Functional inequalities obtained by the comparison of the entropy with the entropy production functional reflect the contraction properties of the flow. Our approach provides a unified framework for the study of the Kolmogorov-Fokker-Planck (KFP) equation. |
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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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| 2 : | Dipartimento di matematica F. Casorati |
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Università degli studi di Pavia |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Optimal transport – Kantorovich-Rubinstein-Wasserstein distance – Generalized Poincaré inequality – Continuity equation – Action functional – Gradient flows – Kolmogorov-Fokker-Planck equation |
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| hal-00595042, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00595042 | |
| oai:hal.archives-ouvertes.fr:hal-00595042 | |
| Contributeur : Jean Dolbeault | |
| Soumis le : Lundi 23 Mai 2011, 11:56:21 | |
| Dernière modification le : Lundi 23 Mai 2011, 16:22:07 | |
