A note on the supersolution method for Hardy's inequality
Francesca Bianchi, Lorenzo Brasco, Firoj Sk, Anna Chiara Zagati
TL;DR
This paper characterizes Hardy's inequality within Sobolev-Slobodecki2f spaces using positive local weak supersolutions, extending prior results for standard Sobolev spaces through variational methods.
Contribution
It introduces a new characterization of Hardy's inequality in Sobolev-Slobodecki2f spaces, broadening the scope of previous work for standard Sobolev spaces.
Findings
Characterization of Hardy's inequality in Sobolev-Slobodecki2f spaces
Extension of previous results by Ancona and Kinnunen & Korte
Use of variational methods for proof
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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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Advanced Mathematical Physics Problems