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dc.contributor.authorToscani, Giuseppe
dc.contributor.authorDolbeault, Jean
dc.date.accessioned2012-07-12T08:08:03Z
dc.date.available2012-07-12T08:08:03Z
dc.date.issued2013
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/9739
dc.language.isoenen
dc.subjectoptimal constantsen
dc.subjectsharp ratesen
dc.subjectintermediate asymptoticsen
dc.subjectsecond momenten
dc.subjectBarenblatt solutionsen
dc.subjectfast diffusion equationen
dc.subjectentropy - entropy production methoden
dc.subjectmanifold of optimal functionsen
dc.subjectimproved inequalitiesen
dc.subjectGagliardo-Nirenberg-Sobolev inequalitiesen
dc.subject.ddc515en
dc.titleImproved interpolation inequalities, relative entropy and fast diffusion equationsen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDipartimento di matematica F. Casorati http://www-dimat.unipv.it/ Università degli studi di Pavia;Italie
dc.description.abstractenWe consider a family of Gagliardo-Nirenberg-Sobolev interpolation inequalities which interpolate between Sobolev's inequality and the logarithmic Sobolev inequality, with optimal constants. The difference of the two terms in the interpolation inequalities (written with optimal constant) measures a distance to the manifold of the optimal functions. We give an explicit estimate of the remainder term and establish an improved inequality, with explicit norms and fully detailed constants. Our approach is based on nonlinear evolution equations and improved entropy - entropy production estimates along the associated flow. Optimizing a relative entropy functional with respect to a scaling parameter, or handling properly second moment estimates, turns out to be the central technical issue. This is a new method in the theory of nonlinear evolution equations, which can be interpreted as the best fit of the solution in the asymptotic regime among all asymptotic profiles.en
dc.relation.isversionofjnlnameAnnales de l'Institut Henri Poincaré. Analyse non linéaire
dc.relation.isversionofjnlvol30
dc.relation.isversionofjnlissue5
dc.relation.isversionofjnldate2013
dc.relation.isversionofjnlpages917-934
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.anihpc.2012.12.004
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00634852en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevier
dc.subject.ddclabelAnalyseen


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