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.
Titolo: | On the capacity approach to non-attainability of Hardy's inequality in $\mathbbR^N$ |
Autori: | RUF, BERNHARD (Secondo) TARSI, CRISTINA (Ultimo) |
Parole Chiave: | functional inequalities; Hardy inequality; Lorentz spaces; Liouville theorems; non-existence results |
Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
Data di pubblicazione: | apr-2019 |
Rivista: | |
Tipologia: | Article (author) |
Digital Object Identifier (DOI): | http://dx.doi.org/10.3934/dcdss.2019017 |
Appare nelle tipologie: | 01 - Articolo su periodico |
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