Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs

Bobo Hua; Ruowei Li

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arXiv · 2411.11071

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs

Bobo Hua·Ruowei Li

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Abstract

We introduce the discrete poly-Laplace operator on a subgraph with Dirichlet boundary condition. We obtain upper and lower bounds for the sum of the first $k$ Dirichlet eigenvalues of the poly-Laplace operators on a finite subgraph of lattice graph $\mathbb{Z}^{d}$ extending classical results of Li-Yau and Kr\"oger. Moreover, we prove that the Dirichlet $2l$-order poly-Laplace eigenvalues are at least as large as the squares of the Dirichlet $l$-order poly-Laplace eigenvalues.

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Bobo Hua, Ruowei Li. 2024-11-17. Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs. https://arxiv.org/abs/2411.11071

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