Boundary Effects on Eigen-problems of Discrete Laplacian in Lattices

Yueh Cheng Kuo, Shih Feng Shieh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 con-ditions. 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.

Original languageEnglish
Pages (from-to)1045-1068
Number of pages24
JournalTaiwanese Journal of Mathematics
Issue number5
Publication statusPublished - 2022 Oct


  • discrete Laplacian
  • eigenvalue gaps
  • eigenvalues

ASJC Scopus subject areas

  • Mathematics(all)


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