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 $\mathbbR^N$ / D. Cassani, B. Ruf, C. Tarsi. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1179. - 12:2(2019 Apr), pp. 245-250. [10.3934/dcdss.2019017]
On the capacity approach to non-attainability of Hardy's inequality in $\mathbbR^N$
B. RufSecondo
;C. TarsiUltimo
2019
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].
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