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arXiv · 1909.12512

On families of optimal Hardy-weights for linear second-order elliptic operators

Yehuda Pinchover·Idan Versano
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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.

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Yehuda Pinchover, Idan Versano. 2019-09-27. On families of optimal Hardy-weights for linear second-order elliptic operators. https://arxiv.org/abs/1909.12512

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