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dc.contributor.authorDolbeault, Jean*
dc.contributor.authorLi, Xingyu*
dc.date.accessioned2019-10-12T12:32:34Z
dc.date.available2019-10-12T12:32:34Z
dc.date.issued2019
dc.identifier.issn1073-7928
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20108
dc.language.isoenen
dc.subjectentropy methods
dc.subjectlogarithmic Hardy-Littlewood-Sobolev inequality
dc.subjectdrift-diffusion-Poisson equation
dc.subjectnonlinear parabolic equations
dc.subject.ddc515en
dc.titleGeneralized logarithmic Hardy-Littlewood-Sobolev inequality
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper is devoted to logarithmic Hardy-Littlewood-Sobolev inequalities in the two-dimensional Euclidean space, in presence of an external potential with logarithmic growth. The coupling with the potential introduces a new parameter, with two regimes. The attractive regime reflects the standard logarithmic Hardy-Littlewood-Sobolev inequality. The second regime corresponds to a reverse inequality, with the opposite sign in the convolution term, that allows us to bound the free energy of a drift-diffusion-Poisson system from below. Our method is based on an extension of an entropy method proposed by E. Carlen, J. Carrillo and M. Loss, and on a nonlinear diffusion equation.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameInternational Mathematics Research Notices
dc.relation.isversionofjnldate2019
dc.relation.isversionofjnlpages9
dc.relation.isversionofdoi10.1093/imrn/rnz32
dc.relation.isversionofjnlpublisherOxford University Press
dc.subject.ddclabelAnalyseen
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dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2020-04-14T09:37:14Z
hal.person.labIds60*
hal.person.labIds60*


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