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arXiv · 2209.03011

A note on the supersolution method for Hardy's inequality

Francesca Bianchi·Lorenzo Brasco·Firoj Sk·Anna Chiara Zagati
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Abstract

We prove a characterization of Hardy's inequality in Sobolev-Slobodecki\u{\i} spaces in terms of positive local weak supersolutions of the relevant Euler-Lagrange equation. This extends previous results by Ancona and Kinnunen & Korte for standard Sobolev spaces. The proof is based on variational methods.

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Francesca Bianchi, Lorenzo Brasco, Firoj Sk, Anna Chiara Zagati. 2022-09-07. A note on the supersolution method for Hardy's inequality. https://arxiv.org/abs/2209.03011

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