On Pleijel's nodal domain theorem for the Robin problem
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914702857076736 |
|---|---|
| author | Hassannezhad, Asma Sher, David |
| author_facet | Hassannezhad, Asma Sher, David |
| contents | We prove an improved Pleijel nodal domain theorem for the Robin eigenvalue problem. In particular we remove the restriction, imposed in previous work, that the Robin parameter be non-negative. We also improve the upper bound in the statement of the Pleijel theorem. In the particular example of a Euclidean ball, we calculate the explicit value of the Pleijel constant for a generic constant Robin parameter and we show that it is equal to the Pleijel constant for the Dirichlet Laplacian on a Euclidean ball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_08094 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Pleijel's nodal domain theorem for the Robin problem Hassannezhad, Asma Sher, David Analysis of PDEs Spectral Theory 35P15, 58J50 We prove an improved Pleijel nodal domain theorem for the Robin eigenvalue problem. In particular we remove the restriction, imposed in previous work, that the Robin parameter be non-negative. We also improve the upper bound in the statement of the Pleijel theorem. In the particular example of a Euclidean ball, we calculate the explicit value of the Pleijel constant for a generic constant Robin parameter and we show that it is equal to the Pleijel constant for the Dirichlet Laplacian on a Euclidean ball. |
| title | On Pleijel's nodal domain theorem for the Robin problem |
| topic | Analysis of PDEs Spectral Theory 35P15, 58J50 |
| url | https://arxiv.org/abs/2303.08094 |