Hardy-type inequalities derived from pp-harmonic problems

We consider the anti-coercive partial differential inequality of elliptic type involving pp-Laplacian: −Δpu≥Φ−Δpu≥Φ, where ΦΦ is a given locally integrable function and uu is defined on an open subset Ω⊆RnΩ⊆Rn. Knowing solutions, we derive Caccioppoli inequalities for uu. As a direct consequence we obtain Hardy inequalities involving certain measures for compactly supported Lipschitz functions. Our methods allow to retrieve classical Hardy inequalities with optimal constants. We present several applications leading to various weighted Hardy inequalities.