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The limit of first
eigenfunctions of the $p$-Laplacian on graphs
Huabin Ge, Bobo Hua and Wenfeng Jiang |
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Vol. 312 (2021), No. 1, 103–112
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Abstract |
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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. |
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Keywords
$p$-Laplacian, graph, isoperimetric inequalities
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Mathematical Subject Classification 2010
Primary: 35R02
Secondary: 35P30
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Milestones
Received: 21 December 2018
Revised: 12 December 2019
Accepted: 29 June 2020
Published: 4 August 2021
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Authors |
| Huabin Ge | |
| School of Mathematics Renmin University of China Beijing 100872 China |
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| Bobo Hua | |
| School of Mathematical Sciences,
LMNS Fudan University Shanghai 200433 China |
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| Wenfeng Jiang | |
| School of Mathematics (Zhuhai) Sun Yat-Sen University Zhuhai 519082 China |
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