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dc.contributor.authorDel Pino, Manuel
dc.contributor.authorDolbeault, Jean
dc.contributor.authorGentil, Ivan
dc.date.accessioned2011-05-09T13:47:00Z
dc.date.available2011-05-09T13:47:00Z
dc.date.issued2004
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6229
dc.language.isoenen
dc.subjectOptimal Lp-Euclidean logarithmic Sobolev inequalityen
dc.subjectSobolev inequalityen
dc.subjectNonlinear parabolic equationsen
dc.subjectDegenerate parabolic problemsen
dc.subjectEntropyen
dc.subjectExistenceen
dc.subjectCauchy problemen
dc.subjectUniquenessen
dc.subjectRegularizationen
dc.subjectHypercontractivityen
dc.subjectUltracontractivityen
dc.subjectLarge deviationsen
dc.subjectHamilton–Jacobi equationsen
dc.subject.ddc515en
dc.titleNonlinear diffusions, hypercontractivity and the optimal Lp-Euclidean logarithmic Sobolev inequalityen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThe 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.isversionofjnlnameJournal of Mathematical Analysis and Applications
dc.relation.isversionofjnlvol293en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2004
dc.relation.isversionofjnlpages375-388en
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.jmaa.2003.10.009en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelAnalyseen


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