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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.26279 |
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| _version_ | 1866911548100837376 |
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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 |