JournalszaaVol. 22, No. 4pp. 757–765

Bounds for the Best Constant in an Improved Hardy-Sobolev Inequality

  • Nirmalendu Chaudhuri

    Australian National University, Canberra, Australia
Bounds for the Best Constant in an Improved Hardy-Sobolev Inequality cover
Download PDF

Abstract

We show that the best constant CC in the improved Hardy-Sobolev inequality of Adimurthi, N. Chaudhuri and M. Ramaswamy [Proc. Amer. Math. Soc. 130 (2002) 489–505] for 2p<n2 \le p < n is bounded by

p1p2(npp)p2Cp12(npp)p2.{p - 1 \over p^2} \big({n - p \over p}\big)^{p-2} \le C \le {p - 1 \over 2} \Big({n - p \over p}\Big)^{p-2}.

Cite this article

Nirmalendu Chaudhuri, Bounds for the Best Constant in an Improved Hardy-Sobolev Inequality. Z. Anal. Anwend. 22 (2003), no. 4, pp. 757–765

DOI 10.4171/ZAA/1171