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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
hal.structure.identifier
dc.contributor.authorGarcia-Huidobro, Marta
hal.structure.identifierCentre de Modélisation Mathématique / Centro de Modelamiento Matemático [CMM]
hal.structure.identifierDepartamento de Ingeniería Matemática [Santiago] [DIM]
dc.contributor.authorManásevich, Raul
dc.date.accessioned2020-01-21T09:57:22Z
dc.date.available2020-01-21T09:57:22Z
dc.date.issued2020
dc.identifier.issn1078-0947
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20447
dc.language.isoenen
dc.subjectrescalingen
dc.subjectperioden
dc.subjectnonlinear Keller-Lieb-Thirring energy estimatesen
dc.subjectbifurcationen
dc.subjectcarré du champ methoden
dc.subjectp-Laplacianen
dc.subjectFisher informationen
dc.subjectentropyen
dc.subjectelliptic equationsen
dc.subjectInterpolationen
dc.subjectGagliardo-Nirenberg inequalitiesen
dc.subjectrigidityen
dc.subjectPoincaré inequalityen
dc.subjectuniquenessen
dc.subjectbranches of solutionsen
dc.subject.ddc515en
dc.titleInterpolation inequalities in W1,p(S1) and carré du champ methodsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper is devoted to an extension of rigidity results for nonlinear differential equations, based on carré du champ methods, in the one-dimensional periodic case. The main result is an interpolation inequality with non-trivial explicit estimates of the constants in W1,p(S1) with p ≥ 2. Mostly for numerical reasons, we relate our estimates with issues concerning periodic dynamical systems. Our interpolation inequalities have a dual formulation in terms of generalized spectral estimates of Keller-Lieb-Thirring type, where the differential operator is now a p-Laplacian type operator. It is remarkable that the carré du champ method adapts to such a nonlinear framework, but significant changes have to be done and, for instance, the underlying parabolic equation has a nonlocal term whenever p≠2.en
dc.relation.isversionofjnlnameDiscrete and Continuous Dynamical Systems. Series A
dc.relation.isversionofjnlvol40en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2020-01
dc.relation.isversionofjnlpages375-394en
dc.relation.isversionofdoi10.3934/dcds.2020014en
dc.relation.isversionofjnlpublisherAIMS - American Institute of Mathematical Sciencesen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2019-12-19T10:54:21Z
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