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hal.structure.identifierInstituto de Ciencias Matemàticas [Madrid] [ICMAT]
dc.contributor.authorBonforte, Matteo
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
hal.structure.identifierStatistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) [SAMM]
dc.contributor.authorNazaret, Bruno
HAL ID: 7130
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorSimonov, Nikita
dc.date.accessioned2021-10-22T11:55:46Z
dc.date.available2021-10-22T11:55:46Z
dc.date.issued2021
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22085
dc.language.isoenen
dc.subjectself-similar Barenblatt solutionsen
dc.subjectintermediate asymptoticsen
dc.subjectasymptotic behavioren
dc.subjectHarnack Principleen
dc.subjectfast diffusion equationen
dc.subjectentropy methodsen
dc.subjectstabilityen
dc.subjectGagliardo-Nirenberg inequalityen
dc.subjectHardy-Poincaré inequalitiesen
dc.subjectspectral gapen
dc.subjectrates of convergenceen
dc.subject.ddc515en
dc.titleStability in Gagliardo-Nirenberg-Sobolev inequalities: flows, regularity and the entropy methoden
dc.typeDocument de travail / Working paper
dc.description.abstractenThe purpose of this work is to establish a quantitative and constructive stability result for a class of subcritical Gagliardo-Nirenberg-Sobolev inequalities which interpolates between the logarithmic Sobolev inequality and the standard Sobolev inequality (in dimension larger than three), or Onofri's inequality in dimension two. We develop a new strategy, in which the flow of the fast diffusion equation is used as a tool: a stability result in the inequality is equivalent to an improved rate of convergence to equilibrium for the flow. The regularity properties of the parabolic flow allow us to connect an improved entropy - entropy production inequality during an initial time layer to spectral properties of a suitable linearized problem which is relevant for the asymptotic time layer. Altogether, the stability in the inequalities is measured by a deficit which controls in strong norms (a Fisher information which can be interpreted as a generalized Heisenberg uncertainty principle) the distance to the manifold of optimal functions. The method is constructive and, for the first time, quantitative estimates of the stability constant are obtained, including in the critical case of Sobolev's inequality. To build the estimates, we establish a quantitative global Harnack principle and perform a detailed analysis of large time asymptotics by entropy methods.en
dc.identifier.citationpages161en
dc.relation.ispartofseriestitleCahier de recherche du CEREMADEen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02887010en
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2021
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2021-10-22T11:51:40Z
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