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Nonlinear flows and rigidity results on compact manifolds

dc.contributor.authorLoss, Michael
dc.contributor.authorEsteban, Maria J.
HAL ID: 738381
ORCID: 0000-0003-1700-9338
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
dc.date.accessioned2013-02-07T14:12:03Z
dc.date.available2013-02-07T14:12:03Z
dc.date.issued2014
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10961
dc.language.isoenen
dc.subjectoptimal constanten
dc.subjectGagliardo-Nirenberg inequalitiesen
dc.subjectinterpolationen
dc.subjectPoincaré inequalityen
dc.subjectSobolev inequalityen
dc.subjectnonlinear diffusionsen
dc.subjectrigidityen
dc.subjectsemilinear elliptic equationsen
dc.subjectRicci tensoren
dc.subjectLaplace-Beltrami operatoren
dc.subjectCompact Riemannian manifolden
dc.subject.ddc515en
dc.titleNonlinear flows and rigidity results on compact manifoldsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper is devoted to rigidity results for some elliptic PDEs and related interpolation inequalities of Sobolev type on smooth compact connected Riemannian manifolds without boundaries. Rigidity means that the PDE has no other solution than the constant one at least when a parameter is in a certain range. This parameter can be used as an estimate for the best constant in the corresponding interpolation inequality. Our approach relies in a nonlinear flow of porous medium / fast diffusion type which gives a clear-cut interpretation of technical choices of exponents done in earlier works. We also establish two integral criteria for rigidity that improve upon known, pointwise conditions, and hold for general manifolds without positivity conditions on the curvature. Using the flow, we are also able to discuss the optimality of the corresponding constant in the interpolation inequalities.en
dc.relation.isversionofjnlnameJournal of Functional Analysis
dc.relation.isversionofjnlvol267
dc.relation.isversionofjnlissue5
dc.relation.isversionofjnldate2014
dc.relation.isversionofjnlpages1338-1363
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.jfa.2014.05.021
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00784887en
dc.relation.isversionofjnlpublisherElsevier
dc.subject.ddclabelAnalyseen
dc.description.submittednonen


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