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Radial symmetry and symmetry breaking for some interpolation inequalities

hal.structure.identifier
dc.contributor.authorTertikas, Achilles*
hal.structure.identifier
dc.contributor.authorTarantello, Gabriella*
hal.structure.identifier
dc.contributor.authorEsteban, Maria J.
HAL ID: 738381
ORCID: 0000-0003-1700-9338		*
hal.structure.identifier
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298		*
dc.date.accessioned2010-09-15T09:03:15Z
dc.date.available2010-09-15T09:03:15Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/4782
dc.language.isoenen
dc.subjectlogarithmic Sobolev inequalityen
dc.subjectKelvin transformationen
dc.subjectcompactnessen
dc.subjectexistenceen
dc.subjectlinearizationen
dc.subjectsymmetry breakingen
dc.subjectradial symmetryen
dc.subjectEmden-Fowler transformationen
dc.subjectscale invarianceen
dc.subjectGagliardo-Nirenberg inequalityen
dc.subjectlogarithmic Hardy inequalityen
dc.subjectCaffarelli-Kohn-Nirenberg inequalityen
dc.subjectHardy-Sobolev inequalityen
dc.subjectinterpolationen
dc.subjectSobolev spacesen
dc.subjectextremal functionsen
dc.subject.ddc515en
dc.titleRadial symmetry and symmetry breaking for some interpolation inequalitiesen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversity of Crete;Grèce
dc.contributor.editoruniversityotherUniversità degli studi di Roma II;Italie
dc.description.abstractenWe analyze the radial symmetry of extremals for a class of interpolation inequalities known as Caffarelli-Kohn-Nirenberg inequalities, and for a class of weighted logarithmic Hardy inequalities which appear as limiting cases of the first ones. In both classes we show that there exists a continuous surface that splits the set of admissible parameters into a region where extremals are symmetric and a region where symmetry breaking occurs. In previous results, the symmetry breaking region was identified by showing the linear instability of the radial extremals. Here we prove that symmetry can be broken even within the set of parameters where radial extremals correspond to local minima for the variational problem associated with the inequality. For interpolation inequalities, such a symmetry breaking phenomenon is entirely new.en
dc.relation.isversionofjnlnameCalculus of Variations and Partial Differential Equations
dc.relation.isversionofjnlvol42
dc.relation.isversionofjnlissue3-4
dc.relation.isversionofjnldate2011
dc.relation.isversionofjnlpages461-485
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00526-011-0394-y
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00516710/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelanalyseen
hal.author.functionaut
hal.author.functionaut
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