Preprint

Inserted: 7 apr 2025
Last Updated: 7 apr 2025

Pages: 25
Year: 2025

Abstract:

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.

Keywords: Laplacian, Robin boundary condition, Negative eigenvalues, Asymptotic expansion, Domains with peaks

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