图上 $p$ 拉普拉斯算子的椭圆梯度估计

IF 0.5 4区 数学 Q3 MATHEMATICS
Lin Feng Wang
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引用次数: 0

摘要

让 $G(V,E)$ 是一个连通的局部有限图。在本文中,我们将考虑方程 ([\Delta_p u - \lambda_p {\lvert u \rvert}^{p-2} u\]on $G$ 的解)的椭圆梯度估计,该方程具有 $\mathrm{CD}^\psi_p (m. -K)$ 条件、-K)$ 条件,其中 $p \geq 2$,$m \gt 0$,$K \geq 0$,并且 $\Delta_p$ 表示 $p\textrm{-}$拉普拉奇。作为应用,我们可以推导出柳维尔定理和哈纳克不等式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Elliptic gradient estimate for the $p$−Laplace operator on the graph
Let $G(V,E)$ be a connected locally finite graph. In this paper we consider the elliptic gradient estimate for solutions to the equation\[\Delta_p u - \lambda_p {\lvert u \rvert}^{p-2} u\]on $G$ with the $\mathrm{CD}^\psi_p (m,-K)$ condition, where $p \geq 2$, $m \gt 0$, $K \geq 0$, and $\Delta_p$ denotes the $p\textrm{-}$Laplacian. As applications, we can derive Liouville theorems and the Harnack inequality.
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来源期刊
CiteScore
1.00
自引率
0.00%
发文量
0
审稿时长
>12 weeks
期刊介绍: Publishes original research papers and survey articles on all areas of pure mathematics and theoretical applied mathematics.
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