Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913579833229312 |
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| author | Hua, Bobo Li, Ruowei |
| author_facet | Hua, Bobo Li, Ruowei |
| contents | 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 Kröger. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11071 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Hua, Bobo Li, Ruowei Spectral Theory Analysis of PDEs Differential Geometry 35J91, 35P15, 05C63, 05C50, 47A75 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 Kröger. 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. |
| title | Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs |
| topic | Spectral Theory Analysis of PDEs Differential Geometry 35J91, 35P15, 05C63, 05C50, 47A75 |
| url | https://arxiv.org/abs/2411.11071 |