Nonradiality of second eigenfunctions of the fractional Laplacian in a ball

2021/02/16 by Jiřı́ Benedikt, В. И. Бобков, Benedikt, Jiří +5 · 1 citation
Computer Science · Mathematics · #35B06 #35P15 #35R11 #47A75 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.2102.08298

openalex publication_date 2021/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using symmetrization techniques, we show that, for every N ≥ 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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• Counterexample to the second eigenfunction having one zero for a non-local Schrodinger operator

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