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The role of Onofri type inequalities in the symmetry properties of extremals for Caffarelli-Kohn-Nirenberg inequalities, in two space dimensions

dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
dc.contributor.authorEsteban, Maria J.
HAL ID: 738381
ORCID: 0000-0003-1700-9338
dc.contributor.authorTarantello, Gabriella
dc.date.accessioned2009-06-18T12:37:31Z
dc.date.available2009-06-18T12:37:31Z
dc.date.issued2008
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/350
dc.language.isoenen
dc.subjectWeighted Moser-Trudinger inequality; Hardy-Sobolev inequality; Onofri's inequality; Caffarelli-Kohn-Nirenberg inequality; extremal functions; Kelvin transformation; Emden-Fowler transformation; stereographic projection; radial symmetry; symmetry breaking; blow-up analysisen
dc.subject.ddc519en
dc.titleThe role of Onofri type inequalities in the symmetry properties of extremals for Caffarelli-Kohn-Nirenberg inequalities, in two space dimensionsen
dc.typeArticle accepté pour publication ou publiéen_US
dc.contributor.editoruniversityotherDipartimento di Matematica Università degli studi di Roma II;Italie
dc.description.abstractenWe first prove a weighted inequality of Moser-Trudinger type depending on a parameter, in the two-dimensional Euclidean space. The inequality holds for radial functions if the parameter is larger than -1. Without symmetry assumption, it holds if and only if the parameter is in the interval (-1,0]. The inequality gives us some insight on the symmetry breaking phenomenon for the extremal functions of the Hardy-Sobolev inequality, as established by Caffarelli-Kohn-Nirenberg, in two space dimensions. In fact, for suitable sets of parameters (asymptotically sharp) we prove symmetry or symmetry breaking by means of a blow-up method. In this way, the weighted Moser-Trudinger inequality appears as a limit case of the Hardy-Sobolev inequality.en
dc.relation.isversionofjnlnameAnnali della Scuola Normale Superiore di Pisa. Classe di Scienze
dc.relation.isversionofjnlvol7en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2008
dc.relation.isversionofjnlpages313–341en
dc.relation.isversionofdoihttp://dx.doi.org/10.2422/2036-2145.2008.2.05en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00139062/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherLe Edizioni della Normaleen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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