Accepted Paper

Inserted: 7 sep 2022
Last Updated: 26 jan 2023

Journal: Rev. Mat. Complut.
Pages: 14
Year: 2022

Abstract:

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

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