Chou, Kai-Seng; Chu, Chiu-Wing On the best constant for a weighted Sobolev-Hardy inequality. (English) Zbl 0739.26013 J. Lond. Math. Soc., II. Ser. 48, No. 1, 137-151 (1993). In this paper the best constant and the functions attaining this constant in the inequality \[ (\int_{\mathbb{R}^ n}| x|^ \alpha| u|^ pdx)^{1/p}\leq C(\int_{\mathbb{R}^ n}| x|^ \beta|\nabla u|^ 2dx)^{1/2} \] for \(p,\alpha\), and \(\beta\) satisfying \(p\geq 2\), \(n+\alpha>0\), \((n+\alpha)/p+1=(n+\beta)/2\), \(\beta/2\geq\alpha/p\), and \(\beta\leq 0\), are determined by an argument involving the method of moving planes. Reviewer: Chou Kai-Seng (Hong Kong) Cited in 1 ReviewCited in 152 Documents MSC: 26D15 Inequalities for sums, series and integrals Keywords:weighted Sobolev-Hardy inequality; best constant; method of moving planes PDFBibTeX XMLCite \textit{K.-S. Chou} and \textit{C.-W. Chu}, J. Lond. Math. Soc., II. Ser. 48, No. 1, 137--151 (1993; Zbl 0739.26013) Full Text: DOI