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dc.contributor.advisor
hal.structure.identifier
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
*
hal.structure.identifier
dc.contributor.authorDel Pino, Manuel*
dc.date.accessioned2011-06-07T08:07:59Z
dc.date.available2011-06-07T08:07:59Z
dc.date.issued1999
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6432
dc.language.isoenen
dc.subjectSobolev embeddingsen
dc.subjectOptimal constantsen
dc.subjectMinimizationen
dc.subjectRadial symmetryen
dc.subjectUniquenessen
dc.subjectFast diffusionen
dc.subjectTime-dependent rescalingen
dc.subjectPorous mediumen
dc.subjectRelative entropyen
dc.subjectOptimal rate of decayen
dc.subjectIntermediate asymptoticsen
dc.subject.ddc515en
dc.titleGeneralized Sobolev Inequalities and Asymptotic Behaviour in Fast Diffusion and Porous Medium Problemsen
dc.typeDocument de travail / Working paper
dc.description.abstractenIn this paper we prove a new family of inequalities which is intermediate between the classical Sobolev inequalities and the Gross logarithmic Sobolev inequality by the minimization of a well choosen functional and the use of recent uniqueness results for the ground state of the corresponding nonlinear scalar field equation, which allows us to identify the optimal constants . This result is then applied to the equation ut = ∆u m in IR for m ∈ [ N , 1[ (fast diffusion) and m > 1 (porous medium), thus giving an exponential rate of decay for the relative entropy to the stationary solution of a rescaled problem and describing the intermediate asymptotics in the L1(IR )-norm.en
dc.publisher.nameUniversité Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages43en
dc.relation.ispartofseriestitleCahiers du CEREMADEen
dc.relation.ispartofseriesnumber1999-05en
dc.description.sponsorshipprivateouien
dc.subject.ddclabelAnalyseen
hal.author.functionaut
hal.author.functionaut


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