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On the capacity approach to non-attainability of Hardy's inequality in $\mathbb{R}^N$

  • * Corresponding author: Daniele Cassani

    * Corresponding author: Daniele Cassani 

In honor of Vicentiu Rădulescu on the occasion of his 60th birthday, with friendship and admiration

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  • 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 $\mathbb{R}^N$, on the other side gives a partial positive answer to a conjecture raised in [15].

    Mathematics Subject Classification: Primary: 35A23; Secondary: 46E30, 35B53.


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