具有CDp⋅(m,K)曲率的加权图上p-拉普拉斯的Hamilton不等式

IF 1.2 3区 数学 Q1 MATHEMATICS
Yongtao Liu
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引用次数: 0

摘要

本文研究了加权图上p-拉普拉斯算子的Hamilton型梯度估计。对于p>;5和一些附加的假设,我们在满足CDp⋅(m,K)曲率的有限图上导出了p-拉普拉斯热方程正解的Hamilton型梯度估计。对于有界加权顶点度的局部有限图也证明了类似的结果。作为我们的主要结果的应用,我们证明了相应的哈纳克不等式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Hamilton inequality for the p-Laplacian on weighted graphs with the CDp⋅(m,K) curvature
In this paper, we study Hamilton type gradient estimates for the p-Laplacian on weighted graphs. For p>5 and some additional assumptions, we derive a more general gradient estimate of Hamilton type for positive solutions to the p-Laplacian heat equation on finite graphs satisfying the CDp(m,K) curvature. The analogous result is also proved for locally finite graphs with bounded weighted vertex degree. As an application of our main results, we show that the corresponding Harnack inequality.
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来源期刊
CiteScore
2.50
自引率
7.70%
发文量
790
审稿时长
6 months
期刊介绍: The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.
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