We are concerned with Sobolev type inequalities in W^{1,p}, on a domain of the n-dimensional Euclidean space, optimal target norms and sharp constants. Admissible remainder terms depending on the gradient are characterized. As a consequence, the strongest possible remainder norm of the gradient is exhibited. Both the case when p < n and the borderline case when p = n are considered. Related Hardy inequalities with remainders are also derived.

Improving sharp Sobolev type inequalities by optimal remainder gradient norms / Andrea Cianchi; Adele Ferone. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 11:(2012), pp. 1385-1408. [10.3934/cpaa.2012.11.1385]

Improving sharp Sobolev type inequalities by optimal remainder gradient norms

CIANCHI, ANDREA;
2012

Abstract

We are concerned with Sobolev type inequalities in W^{1,p}, on a domain of the n-dimensional Euclidean space, optimal target norms and sharp constants. Admissible remainder terms depending on the gradient are characterized. As a consequence, the strongest possible remainder norm of the gradient is exhibited. Both the case when p < n and the borderline case when p = n are considered. Related Hardy inequalities with remainders are also derived.
2012
11
1385
1408
Andrea Cianchi; Adele Ferone
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/786540
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