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<p>We study the asymptotic behavior of individual eigenvalues of the Laplacian in domains with outward peaks for large negative Robin parameters. A large class of cross-sections is allowed, and the resulting asymptotic expansions reflect both the sharpness of the peak and the geometric shape of its cross-section. The results are an extension of previous works dealing with peaks whose cross-sections are balls.</p>

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Laplacian eigenvalues for large negative Robin parameters on domains with outward peaks

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月23日

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  • Konstantin Pankrashkin,
  • Firoj Sk,
  • Marco Vogel

摘要

We study the asymptotic behavior of individual eigenvalues of the Laplacian in domains with outward peaks for large negative Robin parameters. A large class of cross-sections is allowed, and the resulting asymptotic expansions reflect both the sharpness of the peak and the geometric shape of its cross-section. The results are an extension of previous works dealing with peaks whose cross-sections are balls.