整数网格子图上的斯特克洛夫特征值问题

IF 0.7 4区数学 Q2 MATHEMATICS

Communications in Analysis and Geometry Pub Date : 2023-12-06 DOI:10.4310/cag.2023.v31.n2.a4

Wen Han, Bobo Hua

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引用次数: 11

摘要

我们研究了整数网格 $\mathbb{Z}^n$ 的有限子图上的 Dirichlet-to-Neumann 算子的特征值。我们利用子图的顶点数来估计前 $n + 1$ 个特征值。作为推论，我们证明当子图的顶点数趋于无穷大时，Dirichlet-to-Neumann 算子的第一个非三维特征值趋于零。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Steklov eigenvalue problem on subgraphs of integer lattices

We study the eigenvalues of the Dirichlet-to-Neumann operator on a finite subgraph of the integer lattice Zn. We estimate the first n+1 eigenvalues using the number of vertices of the subgraph. As a corollary, we prove that the first non-trivial eigenvalue of the Dirichlet-to-Neumann operator tends to zero as the number of vertices of the subgraph tends to infinity.

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来源期刊

Communications in Analysis and Geometry 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality papers on subjects related to classical analysis, partial differential equations, algebraic geometry, differential geometry, and topology.