Proceedings of the Japan Academy, Series A, Mathematical Sciences

Missing terms in Hardy-Sobolev inequalities

Hiroshi Ando, Alnar Detalla, and Toshio Horiuchi

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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

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

First available in Project Euclid: 18 May 2005

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Zentralblatt MATH identifier

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

Hardy-Sobolev inequality eigenvalue


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.

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