Symmetry of fractional Neumann eigenfunctions in the ball
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915853742637056 |
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| author | Bobkov, Vladimir Parini, Enea |
| author_facet | Bobkov, Vladimir Parini, Enea |
| contents | We investigate symmetry properties of the first nontrivial eigenfunctions of the fractional Laplacian $(-Δ)^s$, where $s \in (0,1)$, in an $N$-dimensional ball with nonlocal Neumann boundary conditions. By means of a spectral stability result, we prove that, when $s$ is sufficiently close to $1$, the eigenspace associated to the first nontrivial eigenvalue is generated by $N$ antisymmetric eigenfunctions with exactly two nodal domains in the ball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10550 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetry of fractional Neumann eigenfunctions in the ball Bobkov, Vladimir Parini, Enea Analysis of PDEs Spectral Theory 35P15, 35R11, 35B06, 47A75 We investigate symmetry properties of the first nontrivial eigenfunctions of the fractional Laplacian $(-Δ)^s$, where $s \in (0,1)$, in an $N$-dimensional ball with nonlocal Neumann boundary conditions. By means of a spectral stability result, we prove that, when $s$ is sufficiently close to $1$, the eigenspace associated to the first nontrivial eigenvalue is generated by $N$ antisymmetric eigenfunctions with exactly two nodal domains in the ball. |
| title | Symmetry of fractional Neumann eigenfunctions in the ball |
| topic | Analysis of PDEs Spectral Theory 35P15, 35R11, 35B06, 47A75 |
| url | https://arxiv.org/abs/2603.10550 |