PreprintCC BY 4.0arXiv
Corner Regularity of Laplacian Eigenfunctions
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.
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BibTeX
@misc{whitton2026corner,
title = {{Corner Regularity of Laplacian Eigenfunctions}},
author = {Finlay Whitton},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09095},
eprint = {2610.09095},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09095},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Corner Regularity of Laplacian Eigenfunctions
AU - Finlay Whitton
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.09095
UR - https://arxiv.org/abs/2610.09095
AB - 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.
ER -