A note on limit of first eigenfunctions of $p$-Laplacian on graphs
Analysis of PDEs
2018-12-20 v1
Abstract
We study the limit of first eigenfunctions of (discrete) -Laplacian on a finite subset of a graph with Dirichlet boundary condition, as We prove that up to a subsequence, they converge to a summation of characteristic functions of Cheeger cuts of the graph. We give an example to show that the limit may not be a characteristic function of a single Cheeger cut.
Keywords
Cite
@article{arxiv.1812.07915,
title = {A note on limit of first eigenfunctions of $p$-Laplacian on graphs},
author = {Huabin Ge and Bobo Hua and Wenfeng Jiang},
journal= {arXiv preprint arXiv:1812.07915},
year = {2018}
}
Comments
10 pages and one figure