Improved Hardy and Rellich inequalities on nonreversible Finsler manifolds

In this paper, we study the sharp constants of quantitative Hardy and Rellich inequalities on nonreversible Finsler manifolds equipped with arbitrary measures. In particular, these inequalities can be globally refined by adding remainder terms like the Brezis–Vázquez improvement, if Finsler manifold...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2018-02, Vol.458 (2), p.1512-1545
Main Authors: Yuan, Lixia, Zhao, Wei, Shen, Yibing
Format: Article
Language:English
Subjects:
Hardy inequality
Nonreversible Finsler manifold
Rellich inequality
Sharp constant
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Summary:In this paper, we study the sharp constants of quantitative Hardy and Rellich inequalities on nonreversible Finsler manifolds equipped with arbitrary measures. In particular, these inequalities can be globally refined by adding remainder terms like the Brezis–Vázquez improvement, if Finsler manifolds are of strictly negative flag curvature, vanishing S-curvature and finite uniformity constant. Furthermore, these results remain valid when Finsler metrics are reversible.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.10.036