Lq Harmonic Functions on Graphs

2013/01/15 by Bobo Hua, Hua, Bobo, Jost, Juergen
Biochemistry, Genetics and Molecular Biology · Mathematics · #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Kruppel-like factors research #Mathematical Physics (math-ph) #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1301.3403

openalex publication_date 2013/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an analogue of Yau's Caccioppoli-type inequality for nonnegative subharmonic functions on graphs. We then obtain a Liouville theorem for harmonic or non-negative subharmonic functions of class Lq, 1<=q 1. Also, we provide counterexamples for Liouville theorems for 0 < q < 1.

Related

• Harmonic functions of general graph Laplacians
• Liouville theorem for bounded harmonic functions on manifolds and graphs satisfying non-negative curvature dimension condition
• A Note on Harmonic Functions on surfaces
• Liouville property and non-negative Ollivier curvature on graphs
• Graphs with positive spectrum