Lq Harmonic Functions on Graphs
Metric Geometry
2013-01-16 v1 Mathematical Physics
math.MP
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<\infty, on any graph, and a quantitative version for q > 1. Also, we provide counterexamples for Liouville theorems for 0 < q < 1.
Keywords
Cite
@article{arxiv.1301.3403,
title = {Lq Harmonic Functions on Graphs},
author = {Bobo Hua and Juergen Jost},
journal= {arXiv preprint arXiv:1301.3403},
year = {2013}
}
Comments
11pages