Show simple item record

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.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.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.isversionofjnlpublisherLe Edizioni della Normaleen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

Files in this item


There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record