On the best possible remaining term in the Hardy Inequality

Abstract

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{${\int }_{\Omega }|\nabla u{|}^{2}dx-(\frac{n-2}{2}{)}^2{\int }_{\Omega }\frac{|u{|}^2}{|x{|}^2}dx\ge c{\int }_{\Omega }V(|x|)|u{|}^{2}dx$ \quad for all $u\in H_0^1(\Omega )$.} \end{equation}

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

Cited by in corpus (10)

• Bessel potentials and optimal Hardy and Hardy-Rellich inequalities
• The best constant in a fractional Hardy inequality
• Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability, and superweights for $L^p$-weighted Hardy inequalities
• Hardy-Poincaré, Rellich and Uncertainty principle inequalities on Riemannian manifolds
• On the critical dimension of a fourth order elliptic problem with negative exponent
• Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials
• Hardy inequalities for general elliptic operators with improvements
• Sobolev inequalities for the Hardy-Schrödinger operator: Extremals and critical dimensions
• On semilinear elliptic equations with borderline Hardy potentials
• Remarks on the Rellich inequality