THE LIMIT OF FIRST EIGENFUNCTIONS OF THE p-LAPLACIAN ON GRAPHS

被引：0

作者：

Ge, Huabin ^{[1
]}

Hua, Bobo ^{[2
]}

Jiang, Wenfeng ^{[3
]}

机构：

[1] Renmin Univ China, Sch Math, Beijing 100872, Peoples R China

[2] Fudan Univ, LMNS, Sch Math Sci, Shanghai 200433, Peoples R China

[3] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Peoples R China

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2021年 / 312卷 / 01期

关键词：

p-Laplacian; graph; isoperimetric inequalities; INEQUALITIES; 1-LAPLACIAN; SPECTRUM;

D O I：

10.2140/pjm.2021.312.103

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the limit of first eigenfunctions of (discrete) p-Laplacian on a finite subset of a graph with Dirichlet boundary condition, as p -> 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.

引用

页码：103 / 112

页数：10

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