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dc.contributor.authorDolbeault, Jean*
dc.contributor.authorEsteban, Maria J.*
dc.contributor.authorLoss, Michael*
dc.date.accessioned2016-07-18T13:03:43Z
dc.date.available2016-07-18T13:03:43Z
dc.date.issued2016
dc.identifier.issn0020-9910
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/15641
dc.language.isoenen
dc.subjectCaffarelli-Kohn-Nirenberg inequalities
dc.subjectsymmetry
dc.subjectsymmetry breaking
dc.subjectoptimal constants
dc.subjectrigidity results
dc.subjectfast diffusion equation
dc.subjectcarré du champ
dc.subjectbifurcation
dc.subjectinstability
dc.subjectEmden-Fowler transformation
dc.subjectcylinders
dc.subjectnon-compact manifolds
dc.subjectLaplace-Beltrami operator
dc.subjectspectral estimates
dc.subjectKeller-Lieb-Thirring estimate
dc.subjectHardy inequality
dc.subject.ddc515en
dc.titleRigidity versus symmetry breaking via nonlinear flows on cylinders and Euclidean spaces
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper is motivated by the characterization of the optimal symmetry breaking region in Caffarelli-Kohn-Nirenberg inequalities. As a consequence, optimal functions and sharp constants are computed in the symmetry region. The result solves a longstanding conjecture on the optimal symmetry range. As a byproduct of our method we obtain sharp estimates for the principal eigenvalue of Schrödinger operators on some non-flat non-compact manifolds, which to the best of our knowledge are new. The method relies on generalized entropy functionals for nonlinear diffusion equations. It opens a new area of research for approaches related to carré du champ methods on non-compact manifolds. However, key estimates depend as much on curvature properties as on purely nonlinear effects. The method is well adapted to functional inequalities involving simple weights and also applies to general cylinders. Beyond results on symmetry and symmetry breaking, and on optimal constants in functional inequalities, rigidity theorems for nonlinear elliptic equations can be deduced in rather general settings.
dc.relation.isversionofjnlnameInventiones Mathematicae
dc.relation.isversionofjnlvol206
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages397-440
dc.relation.isversionofdoi10.1007/s00222-016-0656-6
dc.identifier.urlsitehttp://arxiv.org/abs/1506.03664v1
dc.relation.isversionofjnlpublisherSpringer
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.updated2017-01-03T11:03:59Z
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