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Benedikt, Jiří; Bobkov, Vladimir; Dhara, Raj Narayan; Girg, Petr

Nonradiality of second eigenfunctions of the fractional Laplacian in a ball. (English) Zbl 1498.35018

Proc. Am. Math. Soc. 150, No. 12, 5335-5348 (2022).
Summary: 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.

Cited in 2 Documents

MSC:

35B06 Symmetries, invariants, etc. in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
35P05 General topics in linear spectral theory for PDEs
35R11 Fractional partial differential equations
47A75 Eigenvalue problems for linear operators

Keywords:

symmetrization techniques
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References:

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