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Main Author: Kislitsyn, Aleksei
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2603.26279
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author Kislitsyn, Aleksei
author_facet Kislitsyn, Aleksei
contents 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 $Ω^n$ such that the first Dirichlet eigenfunction for $Ω^n$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_26279
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On Courant-like bound for Neumann domain count
Kislitsyn, Aleksei
Spectral Theory
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 $Ω^n$ such that the first Dirichlet eigenfunction for $Ω^n$ 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.
title On Courant-like bound for Neumann domain count
topic Spectral Theory
url https://arxiv.org/abs/2603.26279