We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
28/2003
Bounds for the Best Constant in an Improved Hardy-Sobolev Inequality
Nirmalendu Chaudhuri
Abstract
In this note we show that the best constant $C$ in the improved Hardy-Sobolev inequality of Adimurthi, Chaudhuri and Ramaswamy [1] for $2\,\leq\,p\,<\,n$, is bounded by ${\displaystyle \frac{p-1}{p^2}\left(\frac{n-p}{p}\right)^{p-2}\,\leq\,C\,\leq\, \frac{p-1}{2}\left(\frac{n-p}{p}\right)^{p-2}}$.