On Courant-like bound for Neumann domain count
Spectral Theory
2026-03-30 v1
Abstract
In this work we show that in general there is no Courant-like bound for Neumann domain count. In order to do that we construct a sequence of domains such that the first Dirichlet eigenfunction for has at least Neumann domains. Also a special case of convex domains is considered and sufficient conditions for existence of Courant-like bound for small eigenvalues are found.
Cite
@article{arxiv.2603.26279,
title = {On Courant-like bound for Neumann domain count},
author = {Aleksei Kislitsyn},
journal= {arXiv preprint arXiv:2603.26279},
year = {2026}
}