Neumann's nodal line may be closed on doubly-connected planar domains
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915913466380288 |
|---|---|
| author | Freitas, Pedro Leylekian, Roméo |
| author_facet | Freitas, Pedro Leylekian, Roméo |
| contents | We show the existence of planar domains with one hole for which the first non-trivial Neumann eigenfunction has a closed nodal line fully contained inside the domain. This is optimal, as it is known since Pleijel's 1956 result that the nodal line cannot be closed on simply-connected planar domains. A part of the proof is based on the study of convergence of eigenvalues and eigenfunctions of graph-like domains towards metric graphs. We improve the known results of convergence of eigenfunctions, by showing a strong transversal convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03169 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Neumann's nodal line may be closed on doubly-connected planar domains Freitas, Pedro Leylekian, Roméo Analysis of PDEs 35J25, 35P05, 35B05 We show the existence of planar domains with one hole for which the first non-trivial Neumann eigenfunction has a closed nodal line fully contained inside the domain. This is optimal, as it is known since Pleijel's 1956 result that the nodal line cannot be closed on simply-connected planar domains. A part of the proof is based on the study of convergence of eigenvalues and eigenfunctions of graph-like domains towards metric graphs. We improve the known results of convergence of eigenfunctions, by showing a strong transversal convergence. |
| title | Neumann's nodal line may be closed on doubly-connected planar domains |
| topic | Analysis of PDEs 35J25, 35P05, 35B05 |
| url | https://arxiv.org/abs/2604.03169 |