Open Access
Oct. 2004 Missing terms in Hardy-Sobolev inequalities
Hiroshi Ando, Alnar Detalla, Toshio Horiuchi
Proc. Japan Acad. Ser. A Math. Sci. 80(8): 160-165 (Oct. 2004). DOI: 10.3792/pjaa.80.160


In this article we shall investigate Hardy-Sobolev inequalities and improve them by adding a term with a singular weight of the type $(\log(1/|x|))^{-2}$. We show that this weight function is optimal in the sense that the inequality fails for any other weight more singular than this one. As an application, we use our improved inequality to study the weighted eigenvalue problem stated in §5.


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Hiroshi Ando. Alnar Detalla. Toshio Horiuchi. "Missing terms in Hardy-Sobolev inequalities." Proc. Japan Acad. Ser. A Math. Sci. 80 (8) 160 - 165, Oct. 2004.


Published: Oct. 2004
First available in Project Euclid: 18 May 2005

zbMATH: 1112.35066
MathSciNet: MR2099744
Digital Object Identifier: 10.3792/pjaa.80.160

Primary: 35J70
Secondary: 35J60

Keywords: eigenvalue , Hardy-Sobolev inequality

Rights: Copyright © 2004 The Japan Academy

Vol.80 • No. 8 • Oct. 2004
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