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January/February 2018 Some improvements for a class of the Caffarelli-Kohn-Nirenberg inequalities
Megumi Sano, Futoshi Takahashi
Differential Integral Equations 31(1/2): 57-74 (January/February 2018).

Abstract

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.

Citation

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Megumi Sano. Futoshi Takahashi. "Some improvements for a class of the Caffarelli-Kohn-Nirenberg inequalities." Differential Integral Equations 31 (1/2) 57 - 74, January/February 2018.

Information

Published: January/February 2018
First available in Project Euclid: 26 October 2017

zbMATH: 06837086
MathSciNet: MR3717734

Subjects:
Primary: 26D10, 35A23

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.31 • No. 1/2 • January/February 2018
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