Global gradient estimate on graph and its applications

Yong Lin Department of Mathematics, Renmin University of China, Beijing, 100872, P. R. China Shuang Liu Department of Mathematics, Renmin University of China, Beijing, 100872, P. R. China Yun Yan Yang Department of Mathematics, Renmin University of China, Beijing, 100872, P. R. China

Differential Geometry mathscidoc:2207.10004

Acta Mathematica Sinica, English Series, 32, 1350–1356, 2016.10
Continuing our previous work (arXiv:1509.07981v1), we derive another global gradient estimate for positive functions, particularly for positive solutions to the heat equation on finite or locally finite graphs. In general, the gradient estimate in the present paper is independent of our previous one. As applications, it can be used to get an upper bound and a lower bound of the heat kernel on locally finite graphs. These global gradient estimates can be compared with the Li–Yau inequality on graphs contributed by Bauer et al. [J. Differential Geom., 99, 359–409 (2015)]. In many topics, such as eigenvalue estimate and heat kernel estimate (not including the Liouville type theorems), replacing the Li–Yau inequality by the global gradient estimate, we can get similar results.
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@inproceedings{yong2016global,
  title={Global gradient estimate on graph and its applications},
  author={Yong Lin, Shuang Liu, and Yun Yan Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707120648185015555},
  booktitle={Acta Mathematica Sinica, English Series},
  volume={32},
  pages={1350–1356},
  year={2016},
}
Yong Lin, Shuang Liu, and Yun Yan Yang. Global gradient estimate on graph and its applications. 2016. Vol. 32. In Acta Mathematica Sinica, English Series. pp.1350–1356. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707120648185015555.
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