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hal.structure.identifier
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
*
hal.structure.identifier
dc.contributor.authorEsteban, Maria J.
HAL ID: 738381
ORCID: 0000-0003-1700-9338
*
hal.structure.identifier
dc.contributor.authorLoss, Michael*
dc.date.accessioned2017-11-27T13:43:05Z
dc.date.available2017-11-27T13:43:05Z
dc.date.issued2016
dc.identifier.issn2296-9020
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17065
dc.language.isoenen
dc.subjectentropy - entropy production inequality
dc.subjectcarré du champ
dc.subjectRényi entropy powers
dc.subjectCaffarelli-Kohn-Nirenberg inequalities
dc.subjectGagliardo-Nirenberg inequalities
dc.subjectweights
dc.subjectoptimal functions
dc.subjectsymmetry
dc.subjectsymmetry breaking
dc.subjectoptimal constants
dc.subjectimproved inequalities
dc.subjectparabolic flows
dc.subjectfast diffusion equation
dc.subjectself-similar solutions
dc.subjectasymptotic behavior
dc.subjectintermediate asymptotics
dc.subjectrate of convergence
dc.subjectentropy methods
dc.subjectself-similar variables
dc.subjectbifurcation
dc.subjectinstability
dc.subjectrigidity results
dc.subjectlinearization
dc.subjectspectral estimates
dc.subjectspectral gap
dc.subjectHardy-Poincaré inequality
dc.subject.ddc515en
dc.titleInterpolation inequalities, nonlinear flows, boundary terms, optimality and linearization
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper is devoted to the computation of the asymptotic boundary terms in entropy methods applied to a fast diffusion equation with weights associated with Caffarelli-Kohn-Nirenberg interpolation inequalities. So far, only elliptic equations have been considered and our goal is to justify, at least partially, an extension of the carré du champ / Bakry-Emery / Rényi entropy methods to parabolic equations. This makes sense because evolution equations are at the core of the heuristics of the method even when only elliptic equations are considered, but this also raises difficult questions on the regularity and on the growth of the solutions in presence of weights.We also investigate the relations between the optimal constant in the entropy–en- tropy production inequality, the optimal constant in the information–information production inequality, the asymptotic growth rate of generalized Rényi entropy powers under the action of the evolution equation and the optimal range of parameters for symmetry breaking issues in Caffarelli-Kohn-Nirenberg inequalities, under the assumption that the weights do not introduce singular boundary terms at x = 0. These considerations are new even in the case without weights. For instance, we establish the equivalence of carré du champ and Rényi entropy methods and explain why entropy methods produce optimal constants in entropy–entropy production and Gagliardo-Nirenberg inequalities in absence of weights, or optimal symmetry ranges when weights are present.
dc.relation.isversionofjnlnameJournal of Elliptic and Parabolic Equations
dc.relation.isversionofjnlvol2
dc.relation.isversionofjnlissue1-2
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages267-295
dc.relation.isversionofdoi10.1007/BF03377405
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-12-19T16:37:31Z
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