
Nonlinear diffusions, hypercontractivity and the optimal Lp-Euclidean logarithmic Sobolev inequality
Del Pino, Manuel; Dolbeault, Jean; Gentil, Ivan (2004), Nonlinear diffusions, hypercontractivity and the optimal Lp-Euclidean logarithmic Sobolev inequality, Journal of Mathematical Analysis and Applications, 293, 2, p. 375-388. http://dx.doi.org/10.1016/j.jmaa.2003.10.009
Type
Article accepté pour publication ou publiéDate
2004Nom de la revue
Journal of Mathematical Analysis and ApplicationsVolume
293Numéro
2Éditeur
Elsevier
Pages
375-388
Identifiant publication
Métadonnées
Afficher la notice complèteRésumé (EN)
The equation ut=Δp(u1/(p−1)) for p>1 is a nonlinear generalization of the heat equation which is also homogeneous, of degree 1. For large time asymptotics, its links with the optimal Lp-Euclidean logarithmic Sobolev inequality have recently been investigated. Here we focus on the existence and the uniqueness of the solutions to the Cauchy problem and on the regularization properties (hypercontractivity and ultracontractivity) of the equation using the Lp-Euclidean logarithmic Sobolev inequality. A large deviation result based on a Hamilton–Jacobi equation and also related to the Lp-Euclidean logarithmic Sobolev inequality is then stated.Mots-clés
Optimal Lp-Euclidean logarithmic Sobolev inequality; Sobolev inequality; Nonlinear parabolic equations; Degenerate parabolic problems; Entropy; Existence; Cauchy problem; Uniqueness; Regularization; Hypercontractivity; Ultracontractivity; Large deviations; Hamilton–Jacobi equationsPublications associées
Affichage des éléments liés par titre et auteur.
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Del Pino, Manuel; Dolbeault, Jean (2003) Article accepté pour publication ou publié
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Del Pino, Manuel; Dolbeault, Jean (2002) Article accepté pour publication ou publié
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Dolbeault, Jean; Gentil, Ivan; Jüngel, Ansgar (2006) Article accepté pour publication ou publié
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Dolbeault, Jean; Del Pino, Manuel (2013) Article accepté pour publication ou publié
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Gentil, Ivan (2009) Communication / Conférence