Best constants in bipolar L^p Hardy-type inequalities

In this work we prove sharp L-p 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 -Delta(p) perturbed by a singular Hardy bipolar potential. (c) 2023 Elsevier Inc. All rights reserved.