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.


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