We show that the classical Hardy inequalities with optimal constants in the Sobolev spaces W1,p 0 and in higher-order Sobolev spaces on a bounded domain ! ! Rn can be refined by adding remainder terms which involve Lp norms. In the higher-order case further Lp norms with lower-order singular weights arise. The case 1 < p < 2 being more involved requires a different technique and is developed only in the space W1,p 0 .
Hardy inequalities with optimal constants and reminder terms / Mitidieri, Enzo; Gazzola, F. GRUNAU H. C.. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 356:(2004), pp. 2149-2168. [10.1090/S0002-9947-03-03395-6]
Hardy inequalities with optimal constants and reminder terms
MITIDIERI, ENZO;
2004-01-01
Abstract
We show that the classical Hardy inequalities with optimal constants in the Sobolev spaces W1,p 0 and in higher-order Sobolev spaces on a bounded domain ! ! Rn can be refined by adding remainder terms which involve Lp norms. In the higher-order case further Lp norms with lower-order singular weights arise. The case 1 < p < 2 being more involved requires a different technique and is developed only in the space W1,p 0 .Pubblicazioni consigliate
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