Geometric Hardy inequalities via integration on flows
Analysis of PDEs
2021-09-20 v2
Abstract
We introduce a geometric approach of integral curves for functional inequalities involving directional derivatives in the general context of differentiable manifolds that are equipped with a volume form. We focus on Hardy-type inequalities and the explicit optimal Hardy potentials that are induced by this method. We then apply the method to retrieve some known inequalities and establish some new ones.
Cite
@article{arxiv.2106.01701,
title = {Geometric Hardy inequalities via integration on flows},
author = {Miltiadis Paschalis},
journal= {arXiv preprint arXiv:2106.01701},
year = {2021}
}