Hardy Type Inequalities Related to Degenerate Elliptic Differential Operators
Abstract
Description
We prove some Hardy type inequalities related to quasilinear second order degenerate elliptic differential operators L_p(u):=-\nabla_L^*(\abs{\nabla_L u}^{p-2}\nabla_L u). If ϕis a positive weight such that -L_pϕ>= 0, then the Hardy type inequality c\int_Ω\frac{\abs u^p}{ϕ^p}\abs{\nabla_L ϕ}^p dξ\le \int_Ω\abs{\nabla_L u}^p dξholds. 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.
37 pages
37 pages