Hardy-type inequalities related to degenerate elliptic differential operators

D’Ambrosio, Lorenzo¹

¹ Dipartimento di Matematica Via E. Orabona, 4 I-70125 Bari, Italy

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 3, pp. 451-486.

Résumé

We prove some Hardy-type inequalities related to quasilinear second-order degenerate elliptic differential operators $L_{p}u:=-{\nabla }_L^{*}\left({\left|{\nabla }_{L}u\right|}^{p-2}{\nabla }_{L}u\right)$. If $\phi$ is a positive weight such that $-L_p\phi \ge 0$, then the Hardy-type inequalityholds. We find an explicit value of the constant involved, which, in most cases, results optimal. As particular case we derive Hardy inequalities for subelliptic operators on Carnot Groups.

Détail

Classification : 35H10, 22E30, 26D10, 46E35

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