Journal of Mathematics of Kyoto University

Missing terms in generalized Hardy’s inequalities and its applications

Toshio Horiuchi

Full-text: Open access


In this article we shall investigate the Hardy inequalities and improve them by finding out missing terms. Although the missing terms for the higher order Hardy inequality can not be determined in a unique way, we shall give a canonical form of the remainder. As a direct application we shall study blow-up solutions of a semilinear elliptic boundary value problem and give some lower estimate of the first eigenvalue of the linearized operator. We also improve the weighted Hardy inequalities, which will be fundamental to study singular solutions of quasilinear elliptic equations.

Article information

J. Math. Kyoto Univ., Volume 43, Number 2 (2003), 235-260.

First available in Project Euclid: 14 August 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26D15: Inequalities for sums, series and integrals
Secondary: 35B45: A priori estimates 35J35: Variational methods for higher-order elliptic equations 35J60: Nonlinear elliptic equations


Horiuchi, Toshio. Missing terms in generalized Hardy’s inequalities and its applications. J. Math. Kyoto Univ. 43 (2003), no. 2, 235--260. doi:10.1215/kjm/1250283727.

Export citation