Effective operators for Robin eigenvalues in domains with corners
Spectral Theory
2021-04-20 v3 Mathematical Physics
Analysis of PDEs
math.MP
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 Schr\"odinger-type operator on the boundary of the domain with boundary conditions at the corners.
Cite
@article{arxiv.1809.04998,
title = {Effective operators for Robin eigenvalues in domains with corners},
author = {Magda Khalile and Thomas Ourmières-Bonafos and Konstantin Pankrashkin},
journal= {arXiv preprint arXiv:1809.04998},
year = {2021}
}
Comments
84 pages. 23 figures. To appear in Annales de l'Institut Fourier (Grenoble)