On Courant-like bound for Neumann domain count

Aleksei Kislitsyn

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arXiv · 2603.26279

On Courant-like bound for Neumann domain count

Aleksei Kislitsyn

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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 $\Omega^n$ such that the first Dirichlet eigenfunction for $\Omega^n$ has at least $n$ 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.

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BibTeX RIS

Aleksei Kislitsyn. 2026-03-27. On Courant-like bound for Neumann domain count. https://arxiv.org/abs/2603.26279

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