Nonradiality of second eigenfunctions of the fractional Laplacian in a ball
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915857927503872 |
|---|---|
| author | Benedikt, Jiří Bobkov, Vladimir Dhara, Raj Narayan Girg, Petr |
| author_facet | Benedikt, Jiří Bobkov, Vladimir Dhara, Raj Narayan Girg, Petr |
| contents | Using symmetrization techniques, we show that, for every $N \geq 2$, any second eigenfunction of the fractional Laplacian in the $N$-dimensional unit ball with homogeneous Dirichlet conditions is nonradial, and hence its nodal set is an equatorial section of the ball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_08298 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Nonradiality of second eigenfunctions of the fractional Laplacian in a ball Benedikt, Jiří Bobkov, Vladimir Dhara, Raj Narayan Girg, Petr Analysis of PDEs Spectral Theory 35P15, 35R11, 35B06, 47A75 Using symmetrization techniques, we show that, for every $N \geq 2$, any second eigenfunction of the fractional Laplacian in the $N$-dimensional unit ball with homogeneous Dirichlet conditions is nonradial, and hence its nodal set is an equatorial section of the ball. |
| title | Nonradiality of second eigenfunctions of the fractional Laplacian in a ball |
| topic | Analysis of PDEs Spectral Theory 35P15, 35R11, 35B06, 47A75 |
| url | https://arxiv.org/abs/2102.08298 |