The eigenvalues of the Laplacian on domains with small slits
Spectral Theory
2008-02-20 v1 Analysis of PDEs
Abstract
We introduce a small slit into a planar domain and study the resulting effect upon the eigenvalues of the Laplacian. In particular, we show that as the length of the slit tends to zero, each real-analytic eigenvalue branch tends to an eigenvalue of the original domain. By combining this with our earlier work (arXiv:math/0703616), we obtain the following application: The generic multiply connected polygon has simple spectrum.
Keywords
Cite
@article{arxiv.0802.2597,
title = {The eigenvalues of the Laplacian on domains with small slits},
author = {Luc Hillairet and Chris Judge},
journal= {arXiv preprint arXiv:0802.2597},
year = {2008}
}
Comments
29 pages, 3 figures