In this paper the question of finding the best constant in a Hardy-Sobolev inequality is addressed. The inequality under investigation gives the possibility to bound a weighted norm of a function u , with a weight which depends only on a group of variables, in terms of the L^p -norm of its gradient. A complete answer is obtained in a special case.
On the best constant in a Hardy-Sobolev inequality / Alvino, Angelo; Ferone, Vincenzo; Trombetti, Guido. - In: APPLICABLE ANALYSIS. - ISSN 0003-6811. - STAMPA. - 85:(2006), pp. 171-180. [10.1080/00036810500277405]
On the best constant in a Hardy-Sobolev inequality
ALVINO, ANGELO;FERONE, VINCENZO;TROMBETTI, GUIDO
2006
Abstract
In this paper the question of finding the best constant in a Hardy-Sobolev inequality is addressed. The inequality under investigation gives the possibility to bound a weighted norm of a function u , with a weight which depends only on a group of variables, in terms of the L^p -norm of its gradient. A complete answer is obtained in a special case.File in questo prodotto:
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