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.File | Dimensione | Formato | |
---|---|---|---|
Cianchi-Ferone_CPAA.pdf
Accesso chiuso
Tipologia:
Versione finale referata (Postprint, Accepted manuscript)
Licenza:
Tutti i diritti riservati
Dimensione
512.62 kB
Formato
Adobe PDF
|
512.62 kB | Adobe PDF | Richiedi una copia |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.