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Improved Poincaré inequalities

dc.contributor.authorVolzone, Bruno
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
dc.date.accessioned2011-11-09T17:54:18Z
dc.date.available2011-11-09T17:54:18Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7432
dc.language.isoenen
dc.subjectWeighted normsen
dc.subjectRemainder termsen
dc.subjectBest constanten
dc.subjectPoincaré inequalityen
dc.subjectHardy inequalityen
dc.subject.ddc515en
dc.titleImproved Poincaré inequalitiesen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDipartimento per le Tecnologie http://www.dit.uniparthenope.it/dit2010/ Università degli Studi di Napoli ''Parthenope'' Università degli Studi di Napoli ''Parthenope'', Facoltà di Ingegneria;Italie
dc.description.abstractenAlthough the Hardy inequality corresponding to one quadratic singularity, with optimal constant, does not admit any extremal function, it is well known that such a potential can be improved, in the sense that a positive term can be added to the quadratic singularity without violating the inequality, and even a whole asymptotic expansion can be build, with optimal constants for each term. This phenomenon has not been much studied for other inequalities. Our purpose is to prove that it also holds for the gaussian Poincaré inequality. The method is based on a recursion formula, which allows to identify the optimal constants in the asymptotic expansion, order by order. We also apply the same strategy to a family of Hardy-Poincaré inequalities which interpolate between Hardy and gaussian Poincaré inequalities.en
dc.relation.isversionofjnlnameNonlinear Analysis: Theory, Methods & Applications
dc.relation.isversionofjnlvol75
dc.relation.isversionofjnlissue16
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages5985–6001
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.na.2012.05.008
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00638281/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevier
dc.subject.ddclabelAnalyseen


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