A note on the first Steklov eigenvalue on planar domains
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915877075550208 |
|---|---|
| author | DelaTorre, Azahara Mancini, Gabriele Pistoia, Angela Provenzano, Luigi |
| author_facet | DelaTorre, Azahara Mancini, Gabriele Pistoia, Angela Provenzano, Luigi |
| contents | We consider the first positive Steklov eigenvalue on planar domains. First, we provide an example of a planar domain for which a first eigenfunction has a closed nodal line. Second, we establish a lower bound for the first positive eigenvalue on certain symmetric domains and show that this eigenvalue is simple for all ellipses. These results complement two statements contained in a work by Kuttler and Sigillito (Proc. Amer. Math. Soc. 20, 1969). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23312 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the first Steklov eigenvalue on planar domains DelaTorre, Azahara Mancini, Gabriele Pistoia, Angela Provenzano, Luigi Analysis of PDEs 35P15, 58C40, 58J50 We consider the first positive Steklov eigenvalue on planar domains. First, we provide an example of a planar domain for which a first eigenfunction has a closed nodal line. Second, we establish a lower bound for the first positive eigenvalue on certain symmetric domains and show that this eigenvalue is simple for all ellipses. These results complement two statements contained in a work by Kuttler and Sigillito (Proc. Amer. Math. Soc. 20, 1969). |
| title | A note on the first Steklov eigenvalue on planar domains |
| topic | Analysis of PDEs 35P15, 58C40, 58J50 |
| url | https://arxiv.org/abs/2507.23312 |