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dc.contributor.authorDolbeault, Jean
dc.contributor.authorMuratori, Matteo
dc.contributor.authorNazaret, Bruno
dc.date.accessioned2016-10-27T07:20:26Z
dc.date.available2016-10-27T07:20:26Z
dc.date.issued2017
dc.identifier.issn0025-5831
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/15900
dc.language.isoenen
dc.subjectFunctional inequalities
dc.subjectWeights
dc.subjectOptimal functions
dc.subjectBest constants
dc.subjectSymmetry
dc.subjectConcentration-compactness
dc.subjectGamma-convergence
dc.subject.ddc515en
dc.titleWeighted interpolation inequalities: a perturbation approach
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherPolitecnico di Milano
dc.contributor.editoruniversityotherUniversité Paris I Panthéon Sorbonne
dc.description.abstractenWe study optimal functions in a family of Caffarelli-Kohn-Niren-berg inequalities with a power-law weight, in a regime for which standardsymmetrization techniques fail. We establish the existence of optimal func-tions, study their properties and prove that they are radialwhen the powerin the weight is small enough. Radial symmetry up to translations is truefor the limiting case where the weight vanishes, a case whichcorresponds toa well-known subfamily of Gagliardo-Nirenberg inequalities. Our approach isbased on a concentration-compactness analysis and on a perturbation methodwhich uses a spectral gap inequality. As a consequence, we prove that optimalfunctions are explicit and given by Barenblatt-type profiles in the perturbativeregime.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameMathematische Annalen
dc.relation.isversionofjnlvol369
dc.relation.isversionofjnlissue3-4
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages1237-1270
dc.relation.isversionofdoi10.1007/s00208-016-1480-4
dc.identifier.urlsitehttp://arxiv.org/abs/1509.09127v1
dc.contributor.countryeditoruniversityotherFRANCE
dc.relation.isversionofjnlpublisherB. G. Teubner
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-10-26T12:58:41Z
hal.person.labIds60
hal.person.labIds5836
hal.person.labIds92163


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