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arXiv · 1812.07915

A note on limit of first eigenfunctions of $p$-Laplacian on graphs

Huabin Ge·Bobo Hua·Wenfeng Jiang
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Abstract

We study the limit of first eigenfunctions of (discrete) $p$-Laplacian on a finite subset of a graph with Dirichlet boundary condition, as $p\to 1.$ 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.

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Huabin Ge, Bobo Hua, Wenfeng Jiang. 2018-12-19. A note on limit of first eigenfunctions of $p$-Laplacian on graphs. https://arxiv.org/abs/1812.07915

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