Hardy's inequality in unbounded domains

Fabrice Colin

DOI: http://dx.doi.org/10.12775/TMNA.2001.016

Abstract


The aim of this paper is to consider Hardy's inequality with
weight on unbounded domains. In particular, using a decomposition
lemma, we study the existence of a minimizer for
$$
S_\varepsilon(\Omega):=
\inf_{u \in D_{\varepsilon}^{1,2}(\Omega)}
\frac {\int_{\Omega}{\vert\nabla u\vert}^2{\delta^{\varepsilon}}dx}
{\int_{\Omega}{\vert u\vert}^2\delta^{\varepsilon - 2}dx}.
$$

Keywords


Hardy's inequality; concentration-compactness; decomposition lemma

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