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October, 2022 Boundary Effects on Eigen-problems of Discrete Laplacian in Lattices
Yueh-Cheng Kuo, Shih-Feng Shieh
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Taiwanese J. Math. 26(5): 1045-1068 (October, 2022). DOI: 10.11650/tjm/220202

Abstract

We consider how distribution of eigenvalues depends on boundary conditions of a discrete Laplacian operator on lattices. We study the Laplacian with boundary conditions given by a linear combination of Dirichlet and Neumann conditions. In particular, we derive a secular equation and investigate the Laplacian operator's eigenvalues with different boundary conditions, including the interlacing property, the first eigenvalue gaps, and the monotonicity property.

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Yueh-Cheng Kuo. Shih-Feng Shieh. "Boundary Effects on Eigen-problems of Discrete Laplacian in Lattices." Taiwanese J. Math. 26 (5) 1045 - 1068, October, 2022. https://doi.org/10.11650/tjm/220202

Information

Received: 19 July 2021; Revised: 13 December 2021; Accepted: 11 February 2022; Published: October, 2022
First available in Project Euclid: 2 March 2022

Digital Object Identifier: 10.11650/tjm/220202

Subjects:
Primary: 34L15 , 93B60

Keywords: discrete Laplacian , eigenvalue gaps , Eigenvalues

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

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Vol.26 • No. 5 • October, 2022
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