On families of optimal Hardy-weights for linear second-order elliptic operators
Analysis of PDEs
2019-09-30 v1 Spectral Theory
Abstract
We construct families of optimal Hardy-weights for a subcritical linear second-order elliptic operator using a one-dimensional reduction. More precisely, we first characterise all optimal Hardy-weights with respect to one-dimensional subcritical Sturm-Liouville operators on a given interval, and then apply this result to obtain families of optimal Hardy inequalities for general linear second-order elliptic operators in higher dimensions. As an application, we prove a new Rellich inequality.
Cite
@article{arxiv.1909.12512,
title = {On families of optimal Hardy-weights for linear second-order elliptic operators},
author = {Yehuda Pinchover and Idan Versano},
journal= {arXiv preprint arXiv:1909.12512},
year = {2019}
}
Comments
24 pages