Effective operators for Robin eigenvalues in domains with corners

Abstract

We study the eigenvalues of the Laplacian with a strong attractive Robin boundary condition in curvilinear polygons. It was known from previous works that the asymptotics of several first eigenvalues is essentially determined by the corner openings, while only rough estimates were available for the next eigenvalues. Under some geometric assumptions, we go beyond the critical eigenvalue number and give a precise asymptotics of any individual eigenvalue by establishing a link with an effective Schrödinger-type operator on the boundary of the domain with boundary conditions at the corners.

arXiv comment84 pages. 23 figures. To appear in Annales de l'Institut Fourier (Grenoble)

References in corpus (2)

• Curvature-induced bound states in Robin waveguides and their asymptotical properties
• On the $p$-Laplacian with Robin boundary conditions and boundary trace theorems

Cited by in corpus (4)

• Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons
• A numerical study of the Dirichlet-to-Neumann operator in planar domains
• Peculiar behavior of the principal Laplacian eigenvalue for large negative Robin parameters
• Laplacian eigenvalues for large negative Robin parameters on domains with outward peaks