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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 ${\displaystyle \frac{p-1}{p^2}\left(\frac{n-p}{p}\right)^{p-2}\,\leq\,C\,\leq\, \frac{p-1}{2}\left(\frac{n-p}{p}\right)^{p-2}}$.

Received:
Mar 24, 2003
Published:
Mar 24, 2003
MSC Codes:
35J
Keywords:
hardy-sobolev ineqality, best constant

Related publications

inJournal
2003 Repository Open Access
Nirmalendu Chaudhuri

Bounds for the best constant in an improved Hardy-Sobolev inequality

In: Zeitschrift fuer Analysis und ihre Anwendungen, 22 (2003) 4, pp. 757-765