On the best possible remaining term in the Hardy Inequality

Details On the best possible remaining term in the Hardy Inequality On the best possible remaining term in the Hardy Inequality

2007-03-16

arxiv.org/abs/math/0703506v1

Mathematics

Analysis of PDEs

13 pages. Updated versions --if any-- of this author's papers can be downloaded at http://pims.math.ca/~nassif/

Scientific paper

10.1073/pnas.0803703105

We give a necessary and sufficient condition on a radially symmetric potential $V$ on $\Omega$ that makes it an admissible candidate for an improved Hardy inequality of the following form: \begin{equation}\label{gen-hardy.0} \hbox{$\int_{\Omega}|\nabla u |^{2}dx - (\frac{n-2}{2})^{2} \int_{\Omega}\frac{|u|^{2}}{|x|^{2}}dx\geq c\int_{\Omega} V(|x|)|u|^{2}dx$ \quad for all $u \in H^{1}_{0}(\Omega)$.} \end{equation}

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