Calculus of Variations and Geometric Measure Theory

F. Bianchi - L. Brasco - F. Sk - A. C. Zagati

A note on the supersolution method for Hardy's inequality

created by bianchi on 07 Sep 2022
modified by brasco on 18 Sep 2022


Submitted Paper

Inserted: 7 sep 2022
Last Updated: 18 sep 2022

Pages: 14
Year: 2022

ArXiv: 2209.03011 PDF


We prove a characterization of Hardy's inequality in Sobolev-Slobodeckii 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: fractional Sobolev spaces, Nonlocal operators, Hardy inequality