Comptes Rendus
Partial Differential Equations
Hardy–Poincaré inequalities and applications to nonlinear diffusions
Comptes Rendus. Mathématique, Volume 344 (2007) no. 7, pp. 431-436.

We systematically study weighted Poincaré type inequalities which are closely connected with Hardy type inequalities and establish the form of the optimal constants in some cases. Such inequalities are then used to relate entropy with entropy production and get intermediate asymptotics results for fast diffusion equations.

Nous étudions des inégalités de Poincaré qui sont étroitement reliées à des inégalités de type Hardy et établissons la forme des constantes optimales dans certains cas. De telles inégalités sont ensuite utilisées pour relier l'entropie avec la production d'entropie et obtenir des résultats d'asymptotiques intermédiaires pour les équations à diffusion rapide.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.01.011
Adrien Blanchet 1; Matteo Bonforte 1; Jean Dolbeault 1; Gabriele Grillo 2; Juan-Luis Vázquez 3

1 CEREMADE, Université Paris Dauphine, place de Lattre de Tassigny, 75775 Paris cedex 16, France
2 Dipartimento di Matematica, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy
3 Departamento de Matemáticas, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049 Madrid, Spain
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Adrien Blanchet; Matteo Bonforte; Jean Dolbeault; Gabriele Grillo; Juan-Luis Vázquez. Hardy–Poincaré inequalities and applications to nonlinear diffusions. Comptes Rendus. Mathématique, Volume 344 (2007) no. 7, pp. 431-436. doi : 10.1016/j.crma.2007.01.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.01.011/

[1] A. Blanchet, M. Bonforte, J. Dolbeault, G. Grillo, J.L. Vázquez, Asymptotics of the fast diffusion equation, in preparation

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[10] J. Denzler; R.J. McCann Fast diffusion to self-similarity: complete spectrum, long-time asymptotics, and numerology, Arch. Ration. Mech. Anal., Volume 175 (2005), pp. 301-342

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