Scholarlink

<p>This paper solves the open problem of the simplicity of the second Dirichlet eigenvalue for nearly equilateral triangles, offering a complete solution to Conjecture 6.47 posed by R. Laugesen and B. Siudeja in A. Henrot’s book “Shape Optimization and Spectral Theory.” Our proof is achieved by introducing a new difference quotient formula for the behavior of nearly degenerate eigenvalues resulting from domain perturbations, and a novel numerical algorithm that rigorously estimates the formula using verified computation.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The second Dirichlet eigenvalue is simple on every non-equilateral triangle, Part ii: Nearly equilateral triangles

  • 期刊论文

  • 发表日期：

    2026年3月30日

查看全文
  • Ryoki Endo,
  • Xuefeng Liu

摘要

This paper solves the open problem of the simplicity of the second Dirichlet eigenvalue for nearly equilateral triangles, offering a complete solution to Conjecture 6.47 posed by R. Laugesen and B. Siudeja in A. Henrot’s book “Shape Optimization and Spectral Theory.” Our proof is achieved by introducing a new difference quotient formula for the behavior of nearly degenerate eigenvalues resulting from domain perturbations, and a novel numerical algorithm that rigorously estimates the formula using verified computation.