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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
dc.date.accessioned2021-10-22T11:46:09Z
dc.date.available2021-10-22T11:46:09Z
dc.date.issued2021
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22084
dc.language.isoenen
dc.subjectGagliardo-Nirenberg inequalityen
dc.subjectCaffarelli-Kohn-Nirenberg inequalityen
dc.subjectstabilityen
dc.subjectentropy methodsen
dc.subjectentropy-entropy production inequalityen
dc.subjectcarré du champen
dc.subjectfast diffusion equationen
dc.subjectHarnack Principleen
dc.subjectasymptotic behaviouren
dc.subjectHardy-Poincaré inequalitiesen
dc.subjectspectral gapen
dc.subjectintermediate asymptoticsen
dc.subjectself-similar Barenblatt solutionsen
dc.subjectrates of convergenceen
dc.subjectsymmetryen
dc.subjectsymmetry breakingen
dc.subjectbifurcationen
dc.subjectInterpolationen
dc.subject.ddc515en
dc.titleFunctional inequalities: nonlinear flows and entropy methods as a tool for obtaining sharp and constructive resultsen
dc.typeDocument de travail / Working paper
dc.description.abstractenInterpolation inequalities play an essential role in Analysis with fundamental consequences in Mathematical Physics, Nonlinear Partial Differential Equations (PDEs), Markov Processes, etc., and have a wide range of applications in various other areas of Science. Research interests have evolved over the years: while mathematicians were originally focussed on abstract properties (for instance appropriate notions of functional spaces for the existence of weak solutions in PDEs), more qualitative questions (for instance, bifurcation diagrams, multiplicity of the solutions in PDEs and their qualitative behaviour) progressively emerged. The use of entropy methods in nonlinear PDEs is a typical example: in some cases, the optimal constant in the inequality can be interpreted as an optimal rate of decay of an entropy for an associated evolution equation. Much more has been learned by adopting this point of view. This paper aims at illustrating some of these recent aspect of entropyentropy production inequalities, with applications to stability in Gagliardo-Nirenberg-Sobolev inequalities and symmetry results in Caffarelli-Kohn-Nirenberg inequalities. Entropy methods provide a framework which relates nonlinear regimes with their linearized counterparts. This framework allows to prove optimality results, symmetry results and stability estimates. Some emphasis will be put on the hidden structure which explain such properties. Related open problems will be listed.en
dc.identifier.citationpages32en
dc.relation.ispartofseriestitleCahier de recherche du CEREMADEen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-03289546en
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2021
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2021-10-22T11:43:56Z
hal.author.functionaut


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