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About existence, symmetry and symmetry breaking for extremal functions of some interpolation functional inequalities

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.accessioned2010-11-29T10:49:35Z
dc.date.available2010-11-29T10:49:35Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/5185
dc.language.isoenen
dc.subjectoptimal constantsen
dc.subjectcompactnessen
dc.subjectexistenceen
dc.subjectlinearizationen
dc.subjectEmden-Fowler transformationen
dc.subjectsymmetry breakingen
dc.subjectradial symmetryen
dc.subjectextremal functionsen
dc.subjectlogarithmic Sobolev inequalityen
dc.subjectlogarithmic Hardy inequalityen
dc.subjectGagliardo-Nirenberg inequalityen
dc.subjectCaffarelli-Kohn-Nirenberg inequalityen
dc.subject.ddc515en
dc.titleAbout existence, symmetry and symmetry breaking for extremal functions of some interpolation functional inequalitiesen
dc.typeChapitre d'ouvrage
dc.description.abstractenThis article is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg (CKN) and weighted logarithmic Hardy (WLH) inequalities. These results have been obtained in a series of papers in collaboration with M. del Pino, S. Filippas, M. Loss, G. Tarantello and A. Tertikas. Here we put the highlights on a symmetry breaking result: extremals of some inequalities are not radially symmetric in regions where the symmetric extremals are linearly stable. Special attention is paid to the study of the critical cases for (CKN) and (WLH).en
dc.identifier.citationpages117-130en
dc.relation.ispartofseriestitleAbel Symposia
dc.relation.ispartofseriesnumbervol.7
dc.relation.ispartoftitleNonlinear Partial Differential Equations - The Abel Symposium 2010
dc.relation.ispartofeditorKarlsen, Kenneth H.
dc.relation.ispartofeditorHolden, Helge
dc.relation.ispartofpublnameSpringer
dc.relation.ispartofpublcityBerlin
dc.relation.ispartofdate2012
dc.relation.ispartofpages360
dc.relation.ispartofurlhttp://dx.doi.org/10.1007/978-3-642-25361-4
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00539019/fr/en
dc.description.sponsorshipprivateouien
dc.subject.ddclabelAnalyseen
dc.relation.ispartofisbn978-3-642-25360-7
dc.identifier.doihttp://dx.doi.org/10.1007/978-3-642-25361-4_6


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