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Sobolev and Hardy-Littlewood-Sobolev inequalities

dc.contributor.authorJankowiak, Gaspard
HAL ID: 2027
ORCID: 0000-0002-9025-1465
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
dc.date.accessioned2013-12-17T12:18:39Z
dc.date.available2013-12-17T12:18:39Z
dc.date.issued2014
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12307
dc.language.isoenen
dc.subjectfast diffusion equationen
dc.subjectstereographic projectionen
dc.subjectbest constantsen
dc.subjectdualityen
dc.subjectextremal functionsen
dc.subjectCaffarelli-Kohn-Nirenberg inequalitiesen
dc.subjectOnofri's inequalityen
dc.subjectlogarithmic Hardy-Littlewood-Sobolev inequalityen
dc.subjectHardy-Littlewood-Sobolev inequalityen
dc.subjectSobolev inequalityen
dc.subjectSobolev spacesen
dc.subject.ddc515en
dc.titleSobolev and Hardy-Littlewood-Sobolev inequalitiesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper is devoted to improvements of Sobolev and Onofri inequalities. The additional terms involve the dual counterparts, i.e. Hardy-Littlewood-Sobolev type inequalities. We focus our attention on optimal constants, that can be achieved either by completion of the square methods or by using nonlinear flows, and provide various new estimates.en
dc.description.abstractenThis paper is devoted to improvements of Sobolev and Onofri inequalities. The additional terms involve the dual counterparts, i.e. Hardy–Littlewood–Sobolev type inequalities. The Onofri inequality is achieved as a limit case of Sobolev type inequalities. Then we focus our attention on the constants in our improved Sobolev inequalities, that can be estimated by completion of the square methods. Our estimates rely on nonlinear flows and spectral problems based on a linearization around optimal Aubin–Talenti functions.
dc.relation.isversionofjnlnameJournal of Differential Equations
dc.relation.isversionofjnlvol257
dc.relation.isversionofjnlissue6
dc.relation.isversionofjnldate2014
dc.relation.isversionofjnlpages1689–1720
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.jde.2014.04.021
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00915998en
dc.relation.isversionofjnlpublisherElsevier
dc.subject.ddclabelAnalyseen
dc.description.submittednonen


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