Dirichlet p-Laplacian eigenvalues and Cheeger constants on symmetric graphs

被引：13

作者：

Hua, Bobo ^{[1
]}

Wang, Lili ^{[2
]}

机构：

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

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

来源：

ADVANCES IN MATHEMATICS | 2020年 / 364卷

基金：

中国博士后科学基金;

关键词：

Dirichlet p-Laplacian; Eigenvalucs; Cheeger constants; Symmetric graphs; 1ST EIGENVALUE; LOWER BOUNDS; 1-LAPLACIAN; INEQUALITIES; MANIFOLDS; EQUATIONS; SPECTRUM; CUT;

D O I：

10.1016/j.aim.2020.106997

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study eigenvalues and eigenfunctions of p-Laplacians with Dirichlet boundary condition on graphs. We characterize the first eigenfunction (and the maximum eigenfunction for a bipartite graph) via the sign condition. By the uniqueness of the first eigenfunction of p-Laplacian, as p -> 1, we identify the Cheeger constant of a symmetric graph with that of the quotient graph. By this approach, we calculate various Cheeger constants of spherically symmetric graphs. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：34

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