English

A note on the supersolution method for Hardy's inequality

Analysis of PDEs 2022-09-08 v1 Functional Analysis

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.

Keywords

Cite

@article{arxiv.2209.03011,
  title  = {A note on the supersolution method for Hardy's inequality},
  author = {Francesca Bianchi and Lorenzo Brasco and Firoj Sk and Anna Chiara Zagati},
  journal= {arXiv preprint arXiv:2209.03011},
  year   = {2022}
}

Comments

14 pages

R2 v1 2026-06-28T00:51:46.724Z