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dc.contributor.authorDolbeault, Jean*
dc.contributor.authorEsteban, Maria J.*
dc.contributor.authorJankowiak, Gaspard*
dc.date.accessioned2014-04-02T13:41:08Z
dc.date.available2014-04-02T13:41:08Z
dc.date.issued2015
dc.identifier.issn0252-9599
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/13034
dc.language.isoenen
dc.subjectMoser-Trudinger-Onofri inequality
dc.subjectDuality
dc.subjectMass transportation
dc.subjectFast diffusion equation
dc.subjectRigidity
dc.subject.ddc515en
dc.titleThe Moser-Trudinger-Onofri inequality
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper is devoted to results on the Moser-Trudinger-Onofri inequality, or Onofri inequality for brevity. In dimension two this inequality plays a role similar to the Sobolev inequality in higher dimensions. After justifying this statement by recovering the Onofri inequality through various limiting procedures and after reviewing some known results, we state several elementary remarks. We also prove various new results. We give a proof of the inequality using mass transportation methods (in the radial case), consistently with similar results for Sobolev's inequalities. We investigate how duality can be used to improve the Onofri inequality, in connection with the logarithmic Hardy-Littlewood-Sobolev inequality. In the framework of fast diffusion equations, we establish that the inequality is an entropy--entropy production inequality, which provides an integral remainder term. Finally we give a proof of the inequality based on rigidity methods and introduce a related nonlinear flow.
dc.relation.isversionofjnlnameChinese Annals of Mathematics. Series B
dc.relation.isversionofjnlvol36
dc.relation.isversionofjnlissue5
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages777-802
dc.relation.isversionofdoi10.1007/s11401-015-0976-7
dc.identifier.urlsitehttps://arxiv.org/abs/1403.5042v3
dc.relation.isversionofjnlpublisherShanghai Scientific and Technological Literature Publishing House
dc.subject.ddclabelAnalyseen
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2016-10-06T15:20:42Z
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