Journal of Mathematics of Kyoto University
- J. Math. Kyoto Univ.
- Volume 43, Number 2 (2003), 235-260.
Missing terms in generalized Hardy’s inequalities and its applications
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.
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. https://projecteuclid.org/euclid.kjm/1250283727