Extremal functions for Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities

Dolbeault, Jean; Esteban, Maria J.

dc.contributor.author	Dolbeault, Jean HAL ID: 87 ORCID: 0000-0003-4234-2298
dc.contributor.author	Esteban, Maria J. HAL ID: 738381 ORCID: 0000-0003-1700-9338
dc.date.accessioned	2010-07-23T15:07:23Z
dc.date.available	2010-07-23T15:07:23Z
dc.date.issued	2012
dc.identifier.uri	https://basepub.dauphine.fr/handle/123456789/4663
dc.language.iso	en	en
dc.subject	Caffarelli-Kohn-Nirenberg inequality	en
dc.subject	Hardy-Sobolev inequality	en
dc.subject	Sobolev spaces	en
dc.subject	existence	en
dc.subject	symmetry breaking	en
dc.subject	compactness	en
dc.subject	radial symmetry	en
dc.subject	Emden-Fowler transformation	en
dc.subject	Kelvin transformation	en
dc.subject	extremal functions	en
dc.subject	logarithmic Hardy inequality	en
dc.subject.ddc	519	en
dc.title	Extremal functions for Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities	en
dc.type	Article accepté pour publication ou publié
dc.description.abstracten	We consider a family of Caffarelli-Kohn-Nirenberg interpolation inequalities and weighted logarithmic Hardy inequalities which have been obtained recently as a limit case of the first ones. We discuss the ranges of the parameters for which the optimal constants are achieved by extremal functions. The comparison of these optimal constants with the optimal constants of Gagliardo-Nirenberg interpolation inequalities and Gross' logarithmic Sobolev inequality, both without weights, gives a general criterion for such an existence result in some particular cases.	en
dc.relation.isversionofjnlname	Proceedings of the Royal Society of Edinburgh. Section A, Mathematical and Physical Sciences
dc.relation.isversionofjnlvol	142
dc.relation.isversionofjnlissue	4
dc.relation.isversionofjnldate	2012
dc.relation.isversionofjnlpages	745-767
dc.relation.isversionofdoi	http://dx.doi.org/10.1017/S0308210510001101
dc.identifier.urlsite	http://hal.archives-ouvertes.fr/hal-00496936/fr/	en
dc.description.sponsorshipprivate	oui	en
dc.relation.isversionofjnlpublisher	Cambridge University Press
dc.subject.ddclabel	Probabilités et mathématiques appliquées	en

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Extremal functions for Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities

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