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On the best constant for a weighted Sobolev-Hardy inequality. (English) Zbl 0739.26013

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.

MSC:

26D15 Inequalities for sums, series and integrals
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