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SOME $\boldsymbol {L^p}$-HARDY AND $\boldsymbol {L^p}$-RELLICH TYPE INEQUALITIES WITH REMAINDER TERMS

Part of: Global differential geometry Inequalities

Published online by Cambridge University Press:  22 June 2021

YONGYANG JIN  and
SHOUFENG SHEN
YONGYANG JIN
Affiliation:
Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310032, PR China e-mail: yongyang@zjut.edu.cn
SHOUFENG SHEN*
Affiliation:
Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310032, PR China
*
e-mail: mathssf@zjut.edu.cn
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Abstract

In this paper we obtain some improved $L^p$ -Hardy and $L^p$ -Rellich inequalities on bounded domains of Riemannian manifolds. For Cartan–Hadamard manifolds we prove the inequalities with sharp constants and with weights being hyperbolic functions of the Riemannian distance.

Keywords

best constantsHardy inequalityRellich inequalityRiemannian manifolds

MSC classification

Primary: 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 113 , Issue 1 , August 2022 , pp. 79 - 98
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by Graeme Wilkin

The authors were supported by NNSF of China (11771395, 12071431).

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