In this note we exploit nonlinear capacity estimates in the spirit of Mitidieri-Pohozaev [15] in the context of Lorentz spaces. This from one side yields a simple proof, though non-optimal, of non-attainability of Hardy's inequality in RN, on the other side gives a partial positive answer to a conjecture raised in [15].

On the capacity approach to non-attainability of Hardy’s inequality in Rn

Daniele Cassani
;
2019-01-01

Abstract

In this note we exploit nonlinear capacity estimates in the spirit of Mitidieri-Pohozaev [15] in the context of Lorentz spaces. This from one side yields a simple proof, though non-optimal, of non-attainability of Hardy's inequality in RN, on the other side gives a partial positive answer to a conjecture raised in [15].
2019
Functional inequalities; Hardy inequality; Liouville theorems; Lorentz spaces; Non-existence results;
Cassani, Daniele; Tarsi, Cristina; Ruf, Bernhard
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2074677
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