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dc.contributor.authorDolbeault, Jean*
dc.contributor.authorEsteban, Maria J.*
dc.contributor.authorLoss, Michael*
dc.contributor.authorMuratori, Matteo*
dc.date.accessioned2017-11-27T11:08:47Z
dc.date.available2017-11-27T11:08:47Z
dc.date.issued2017
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17055
dc.language.isoenen
dc.subjectEmden-Fowler transformation
dc.subjectcarré du champ
dc.subjectfast diffusion equation
dc.subjectflows
dc.subjectsemilinear elliptic equations
dc.subjectsymmetry breaking
dc.subjectsymmetry
dc.subjectbest constants
dc.subjectoptimal functions
dc.subjectuniqueness
dc.subjectrigidity results
dc.subjectFunctional inequalities
dc.subjectinterpolation
dc.subjectCaffarelli-Kohn-Nirenberg inequalities
dc.subjectweights
dc.subject.ddc515en
dc.titleSymmetry for extremal functions in subcritical Caffarelli-Kohn-Nirenberg inequalities
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe use the formalism of the Rényi entropies to establish the symmetry range of extremal functions in a family of subcriti-cal Caffarelli-Kohn-Nirenberg inequalities. By extremal functions we mean functions which realize the equality case in the inequalities, written with optimal constants. The method extends recent results on critical Caffarelli-Kohn-Nirenberg inequalities. Using heuristics given by a nonlinear diffusion equation, we give a variational proof of a symmetry result, by establishing a rigidity theorem: in the symmetry region, all positive critical points have radial symmetry and are therefore equal to the unique positive, radial critical point, up to scalings and multiplications. This result is sharp. The condition on the parameters is indeed complementary of the condition which determines the region in which symmetry breaking holds as a consequence of the linear instability of radial optimal functions. Compared to the critical case, the subcritical range requires new tools. The Fisher information has to be replaced by Rényi entropy powers, and since some invariances are lost, the estimates based on the Emden-Fowler transformation have to be modified.
dc.relation.isversionofjnlnameComptes rendus - Mathematique
dc.relation.isversionofjnlvol355
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages133-154
dc.relation.isversionofdoi10.1016/j.crma.2017.01.004
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.updated2017-12-08T16:38:44Z
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