Differential and Integral Equations
- Differential Integral Equations
- Volume 31, Number 1/2 (2018), 57-74.
Some improvements for a class of the Caffarelli-Kohn-Nirenberg inequalities
In this paper, we concern a weighted version of the Hardy inequality, which is a special case of the more general Caffarelli-Kohn-Nirenberg inequalities. We improve the inequality on the whole space or on a bounded domain by adding various remainder terms. On the whole space, we show the existence of a remainder term which has the form of ratio of two weighted integrals. Also we give a simple derivation of the remainder term involving a distance from the manifold of the “virtual extremals”. Finally, on a bounded domain, we prove the existence of remainder terms involving the gradient of functions.
Differential Integral Equations Volume 31, Number 1/2 (2018), 57-74.
First available in Project Euclid: 26 October 2017
Permanent link to this document
Primary: 35A23: Inequalities involving derivatives and differential and integral operators, inequalities for integrals 26D10: Inequalities involving derivatives and differential and integral operators
Sano, Megumi; Takahashi, Futoshi. Some improvements for a class of the Caffarelli-Kohn-Nirenberg inequalities. Differential Integral Equations 31 (2018), no. 1/2, 57--74. https://projecteuclid.org/euclid.die/1509041401