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Israel Journal of Mathematics

, Volume 202, Issue 1, pp 475–490 | Cite as

L q harmonic functions on graphs

  • Bobo HuaEmail author
  • Jürgen Jost
Article

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 nonnegative subharmonic functions of class L q , 1 ≤ q < ∞, on any graph, and a quantitative version for q > 1. Also, we provide counterexamples for Liouville theorems for 0 < q < 1.

Keywords

Harmonic Function Edge Weight Weighted Graph Subharmonic Function Complete Riemannian Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University of Jerusalem 2014

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Department of Mathematics and Computer ScienceUniversity of LeipzigLeipzigGermany

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