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arXiv · 2603.10550

Symmetry of fractional Neumann eigenfunctions in the ball

Vladimir Bobkov·Enea Parini
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Abstract

We investigate symmetry properties of the first nontrivial eigenfunctions of the fractional Laplacian $(-\Delta)^s$, 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.

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Vladimir Bobkov, Enea Parini. 2026-03-11. Symmetry of fractional Neumann eigenfunctions in the ball. https://arxiv.org/abs/2603.10550

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