Cahiers du CEREMADE 

Unité
Mixte de Recherche du C.N.R.S. N°7534 

Abstract : We first prove a weighted inequality of MoserTrudinger type depending on a parameter, in the twodimensional 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 HardySobolev inequality, as established by CaffarelliKohnNirenberg, in two space dimensions. In fact, for suitable sets of parameters (asymptotically sharp) we prove symmetry or symmetry breaking by means of a blowup method. In this way, the weighted MoserTrudinger inequality appears as a limit case of the HardySobolev inequality. 





200711 

29032007 

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