## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Missing terms in Hardy-Sobolev inequalities

#### Abstract

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.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 80, Number 8 (2004), 160-165.

Dates
First available in Project Euclid: 18 May 2005

https://projecteuclid.org/euclid.pja/1116442375

Digital Object Identifier
doi:10.3792/pjaa.80.160

Mathematical Reviews number (MathSciNet)
MR2099744

Zentralblatt MATH identifier
1112.35066

Subjects
Primary: 35J70: Degenerate elliptic equations
Secondary: 35J60: Nonlinear elliptic equations

#### Citation

Detalla, Alnar; Horiuchi, Toshio; Ando, Hiroshi. Missing terms in Hardy-Sobolev inequalities. Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 8, 160--165. doi:10.3792/pjaa.80.160. https://projecteuclid.org/euclid.pja/1116442375

#### References

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