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Missing terms in Hardy-Sobolev inequalities. (English) Zbl 1112.35066

The aim of this paper is to achieve an optimal improvement of Hardy-Sobolev inequality, by adding a second term involving the singular weight \((\log(1/\left| x\right| ))^{-2}\), in the sense that the improved inequality holds for this weight but fails for any weight more singular than this one.

MSC:

35J60 Nonlinear elliptic equations
26D15 Inequalities for sums, series and integrals
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