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

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.

32 pages, 2 figures

References in corpus (6)

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• On the negative spectrum of the Robin Laplacian in corner domains
• Robin eigenvalues on domains with peaks
• Effective operators for Robin eigenvalues in domains with corners
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• Peculiar behavior of the principal Laplacian eigenvalue for large negative Robin parameters