Hardy-type inequalities related to degenerate elliptic differential operators

Abstract

We prove some Hardy-type inequalities related to quasilinear second-order degenerate elliptic differential operators L pu := -∇*L* ( ∇ Lu p-2∇Lu). If φ is a positive weight such that - L pφ ≥ 0, then the Hardy-type inequality c ∫Ω φP/ u P ∇ Lφ P d ξ ≤ ∫ Ω ∇ Lu P dξ (u ε 01 (Ω)) holds. 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.