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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.authorJankowiak, Gaspard
HAL ID: 2027
ORCID: 0000-0002-9025-1465
*
dc.date.accessioned2017-11-27T11:26:41Z
dc.date.available2017-11-27T11:26:41Z
dc.date.issued2017
dc.identifier.issn1078-0947
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17057
dc.language.isoenen
dc.subjectoptimal constant
dc.subjectPoincaré inequality
dc.subjectSobolev inequality
dc.subjectcarré du champ
dc.subjectrigidity
dc.subjectsemilinear elliptic equation
dc.subjectRicci tensor
dc.subjectnonlinear diffusion
dc.subjectuniqueness
dc.subjectMoser-Trudinger-Onofri inequality
dc.subjectcompact Riemannian manifold
dc.subjectLaplace-Beltrami operator
dc.subject.ddc515en
dc.titleOnofri inequalities and rigidity results
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper is devoted to the Moser-Trudinger-Onofri inequality on smooth compact connected Riemannian manifolds. We establish a rigidity result for the Euler-Lagrange equation and deduce an estimate of the optimal constant in the inequality on two-dimensional closed Riemannian manifolds. Compared to existing results, we provide a non-local criterion which is well adapted to variational methods, introduce a nonlinear flow along which the evolution of a functional related with the inequality is monotone and get an integral remainder term which allows us to discuss optimality issues. As an important application of our method, we also consider the non-compact case of the Moser-Trudinger-Onofri inequality on the two-dimensional Euclidean space, with weights. The standard weight is the one that is computed when projecting the two-dimensional sphere using the stereographic projection, but we also give more general results which are of interest, for instance, for the Keller-Segel model in chemotaxis.
dc.relation.isversionofjnlnameDiscrete and Continuous Dynamical Systems. Series A
dc.relation.isversionofjnlvol37
dc.relation.isversionofjnlissue6
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages3059-3078
dc.relation.isversionofdoi10.3934/dcds.2017131
dc.relation.isversionofjnlpublisherDept. of Mathematics
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.updated2017-12-12T13:39:17Z
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