Inserted: 7 sep 2022
Last Updated: 26 jan 2023
Journal: Rev. Mat. Complut.
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