Bochner formula and Bernstein type estimates on locally finite graphs

2013/04/01 by Li Ma, Ma, Li
Mathematics · #05C50 #35Jxx #53Cxx #68R10 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1304.0290

openalex publication_date 2013/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider three typical problems on a locally finite connected graph. The first one is to study the Bochner formula for the Laplacian operator on a locally finite connected graph. We use the Bochner formula to derive the Bernstein type estimate of the heat equation. The second is to derive the Reilly type formula of the Laplacian operator. The last one is to obtain global positive solution to porous-media equation via the use of Aronson-Benilan argument. There is not much work in the direction of the study of nonlinear heat equations on locally finite connected graphs.

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