Eigenvalue estimate for the p $p$ -Laplace operator on a connected finite graph

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-05-23 DOI:10.1112/blms.70104

Lin Feng Wang

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Abstract

In this paper, we consider eigenvalue estimate for the $p$ -Laplace operator $▵_{p}$ on a connected finite graph with the ${CD}_{p} (m, 0)$ condition for $p > 1$ and $m > 0$ . We first establish elliptic gradient estimates for solutions to the eigenvalue equation. Then we establish a lower bound estimate for the first nonzero eigenvalue of $▵_{p}$ , which is a generalization not only of the eigenvalue estimate for the manifold setting, but also of the eigenvalue estimate for the $μ$ -Laplace operator $▵_{μ}$ on the graph with the $CD (m, 0)$ condition.

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连通有限图上p$ p$ -拉普拉斯算子的特征值估计

本文研究了具有CD p (m)的连通有限图上p$ p$ -拉普拉斯算子p_p $\三角形_p$的特征值估计0)$ \ mathm {CD}_p(m,0)$ condition for p >；1$ and m >；0$ m>0$。我们首先建立了特征值方程解的椭圆梯度估计。然后，我们建立了第一个非零特征值的下界估计，该估计不仅是流形设定的特征值估计的推广，也讨论了μ $\mu$ -拉普拉斯算子在具有CD (m,0)$ \mathrm{CD}(m,0)$条件的图上的μ $\triangle _{\mu}$的特征值估计。

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