Harnack and mean value inequalities on graphs

Yong Lin Department of Mathematics, Renmin University of China, Beijing 100872, China Hongye Song School of General Education, Beijing International Studies University, Beijing 100024, China; Department of Mathematics, Renmin University of China, Beijing 100872, China

Analysis of PDEs Differential Geometry mathscidoc:2207.03005

Acta Mathematica Scientia, 38, (6), 1751-1758, 2018.11
We prove a Harnack inequality for positive harmonic functions on graphs which is similar to a classical result of Yau on Riemannian manifolds. Also, we prove a mean value inequality of nonnegative subharmonic functions on graphs.
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@inproceedings{yong2018harnack,
  title={Harnack and mean value inequalities on graphs},
  author={Yong Lin, and Hongye Song},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707152411831663562},
  booktitle={Acta Mathematica Scientia},
  volume={38},
  number={6},
  pages={1751-1758},
  year={2018},
}
Yong Lin, and Hongye Song. Harnack and mean value inequalities on graphs. 2018. Vol. 38. In Acta Mathematica Scientia. pp.1751-1758. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707152411831663562.
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