Harmonic functions of general graph Laplacians |
| |
Authors: | Bobo Hua Matthias Keller |
| |
Affiliation: | 1. Max Planck Institute for Mathematics in the Sciences, 04103?, Leipzig, Germany 2. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, 91904?, Jerusalem, Israel
|
| |
Abstract: | We study harmonic functions on general weighted graphs which allow for a compatible intrinsic metric. We prove an (L^{p}) Liouville type theorem which is a quantitative integral (L^{p}) estimate of harmonic functions analogous to Karp’s theorem for Riemannian manifolds. As corollaries we obtain Yau’s (L^{p}) -Liouville type theorem on graphs, identify the domain of the generator of the semigroup on (L^{p}) and get a criterion for recurrence. As a side product, we show an analogue of Yau’s (L^{p}) Caccioppoli inequality. Furthermore, we derive various Liouville type results for harmonic functions on graphs and harmonic maps from graphs into Hadamard spaces. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|