图上的Li-Yau不等式的一些注记

林勇, 满守东

数学学报 ›› 2015, Vol. 58 ›› Issue (6) : 953-964.

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数学学报 ›› 2015, Vol. 58 ›› Issue (6) : 953-964. DOI: 10.12386/A2015sxxb0094
论文

图上的Li-Yau不等式的一些注记

    林勇1, 满守东2
作者信息 +

Some Remarks on Li–Yau Inequality on Graphs

    Yong LIN1, Shou Dong MAN2
Author information +
文章历史 +

摘要

对于图G上热方程(Δ-∂/∂t-q)u=0的正解u=u(x,t),得到图上改进的Li-Yau 梯度估计不等式,这里 q 满足Γ(q)≤ η2, η 是一个常数,进而得到改进的 Harnack型不等式, 推广了以前的结果.

Abstract

We obtain improved Li–Yau gradient estimates on graphs for the solutions u to the general heat equation (Δ - ∂/∂t - q)u = 0, where q is a potential satisfying Γ(q) ≤ η2 and η is a constant, and get Harnack inequalities, extending previous results.

关键词

Li-Yau 不等式 / 热方程 / 梯度估计 / 曲率

Key words

Li–Yau inequality / heat equation / gradient estimate / curvature

引用本文

导出引用
林勇, 满守东. 图上的Li-Yau不等式的一些注记. 数学学报, 2015, 58(6): 953-964 https://doi.org/10.12386/A2015sxxb0094
Yong LIN, Shou Dong MAN. Some Remarks on Li–Yau Inequality on Graphs. Acta Mathematica Sinica, Chinese Series, 2015, 58(6): 953-964 https://doi.org/10.12386/A2015sxxb0094

参考文献

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[2] Bauer F., Horn P., Lin Y., et al., Li–Yau inequality on graphs, Arxiv: 1306.2561v2.

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[8] Li X. D., Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds, J. Math. Pures Appl., 2005, 84: 1295–1361.

[9] Lin Y., Yau S. T., Ricci curvature and eigenvalue estimate on locally finite graphs, Math. Res. Lett., 2010, 17: 343–356.

[10] Ma L., Gradient estimates for a simple elliptic equation on complete non-compact Riemannian manifolds, J. Funct. Anal., 2006, 241: 374–382.

[11] Qian B., Remarks on Li–Yau inequality on graphs, arXiv: 1311.3367.

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基金

国家自然科学基金资助项目(11271011);中国人民大学科学研究基金:中央高校基本科研业务费专项资金资助项目(11XN1004)

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