Nonlinear diffusions, hypercontractivity and the optimal Lp-Euclidean logarithmic Sobolev inequality

Del Pino, Manuel; Dolbeault, Jean; Gentil, Ivan

dc.contributor.author	Del Pino, Manuel
dc.contributor.author	Dolbeault, Jean HAL ID: 87 ORCID: 0000-0003-4234-2298
dc.contributor.author	Gentil, Ivan
dc.date.accessioned	2011-05-09T13:47:00Z
dc.date.available	2011-05-09T13:47:00Z
dc.date.issued	2004
dc.identifier.uri	https://basepub.dauphine.fr/handle/123456789/6229
dc.language.iso	en	en
dc.subject	Optimal Lp-Euclidean logarithmic Sobolev inequality	en
dc.subject	Sobolev inequality	en
dc.subject	Nonlinear parabolic equations	en
dc.subject	Degenerate parabolic problems	en
dc.subject	Entropy	en
dc.subject	Existence	en
dc.subject	Cauchy problem	en
dc.subject	Uniqueness	en
dc.subject	Regularization	en
dc.subject	Hypercontractivity	en
dc.subject	Ultracontractivity	en
dc.subject	Large deviations	en
dc.subject	Hamilton–Jacobi equations	en
dc.subject.ddc	515	en
dc.title	Nonlinear diffusions, hypercontractivity and the optimal Lp-Euclidean logarithmic Sobolev inequality	en
dc.type	Article accepté pour publication ou publié
dc.description.abstracten	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.	en
dc.relation.isversionofjnlname	Journal of Mathematical Analysis and Applications
dc.relation.isversionofjnlvol	293	en
dc.relation.isversionofjnlissue	2	en
dc.relation.isversionofjnldate	2004
dc.relation.isversionofjnlpages	375-388	en
dc.relation.isversionofdoi	http://dx.doi.org/10.1016/j.jmaa.2003.10.009	en
dc.description.sponsorshipprivate	oui	en
dc.relation.isversionofjnlpublisher	Elsevier	en
dc.subject.ddclabel	Analyse	en