English

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) pp-Laplacian on a finite subset of a graph with Dirichlet boundary condition, as p1.p\to 1. 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