Best constants in bipolar Lp Hardy-type inequalities

Abstract

In this work we prove sharp Lp versions of the multipolar Hardy inequalities in [8,10], in the case of a bipolar potential and p≥2. Our results are sharp and minimizers do exist in the energy space. New features appear when p>2 compared to the linear case p=2 at the level of criticality of the p-Laplacian −Δp perturbed by a singular Hardy bipolar potential.