Year: 2026
Type: preprint
Abstract: We study the regularity of eigenfunctions of the Dirichlet Laplacian on domains with corners. The specific question we consider is whether the eigenfunctions can be smooth, e.g. trigonometric, on the closure of their domain. We determine how this regularity depends on the local geometry of the corner. Local asymptotic analysis provides detailed information about eigenfunctions near corners and allows us to quantify the Hölder regularity of the normal derivative. We demonstrate the limitations of some of the methods used to study these problems in finding a complete set of eigenvalues on polygons.
Source: arXiv (Cornell University)
Author: Whitton, Finlay
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221056241