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Hardy-type inequalities related to degenerate elliptic differential operators

Lorenzo D’Ambrosio — 2005

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove some Hardy-type inequalities related to quasilinear second-order degenerate elliptic differential operators L p u : = - L * ( L u p - 2 L u ) . If φ is a positive weight such that - L p φ 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.

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