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arXiv · 2102.08298

Nonradiality of second eigenfunctions of the fractional Laplacian in a ball

Jiří Benedikt·Vladimir Bobkov·Raj Narayan Dhara·Petr Girg
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Abstract

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.

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Jiří Benedikt, Vladimir Bobkov, Raj Narayan Dhara, Petr Girg. 2021-02-16. Nonradiality of second eigenfunctions of the fractional Laplacian in a ball. https://doi.org/10.1090/proc/16062

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