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dc.contributor.authorBonforte, Matteo
dc.contributor.authorGrillo, Gabriele
dc.date.accessioned2014-06-02T08:28:53Z
dc.date.available2014-06-02T08:28:53Z
dc.date.issued2007
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/13397
dc.language.isoenen
dc.subjectSingular evolutionsen
dc.subjectRiemannian manifoldsen
dc.subjectSobolev inequalitiesen
dc.subjectsmoothing effecten
dc.subject.ddc515en
dc.titleSingular evolution on maniforlds, their smoothing properties, and Sobolev inequalitiesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThe evolution equation [u_ = \Delta_pu] , posed on a Riemannian manifold, is studied in the singular range [p \in 2] (1; 2). It is shown that if the manifold supports a suitable Sobolev inequality, the smoothing effect [||u(t)||\infty\leq C ||u(0)||_q^\gamma] / [t^\alpha] holds true for suitable for [\alpha, \gamma] and that the converse holds if [p] is sufficiently close to 2, or in the degenerate range [p] > 2. In such ranges, the Sobolev inequality and the smoothing efect are then equivalent .en
dc.relation.isversionofjnlnameDiscrete and Continuous Dynamical Systems. Series A
dc.relation.isversionofjnldate2007
dc.relation.isversionofjnlpages130-137en
dc.relation.isversionofdoihttp://dx.doi.org/10.3934/proc.2007.2007.130en
dc.relation.isversionofjnlpublisherAIMSen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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