Caccioppoli-type estimates and Hardy-type inequalities derived from weighted p-harmonic problems

Abstract

We obtain Caccioppoli-type estimates for nontrivial and nonnegative solutions to anticoercive partial differential inequalities of elliptic type involving weighted p-Laplacian: − p,a u := −div(a(x)|∇u| p−2 ∇u) ≥ b(x) (u)χ {u>0} , where u is defined in a domain. Using Caccioppoli-type estimates, we obtain several variants of Hardy-type inequalities in weighted Sobolev spaces.