Anti-symmetry of the second eigenfunction of the fractional Laplace operator in a 3-D ball

TL;DR

This paper extends a recent mathematical result regarding the symmetry properties of the second eigenfunction of the fractional Laplace operator from lower dimensions to three-dimensional space, enhancing understanding of fractional PDEs.

Contribution

It generalizes the anti-symmetry property of the second eigenfunction of the fractional Laplacian to three dimensions, building on previous two-dimensional results.

Findings

Proves anti-symmetry of the second eigenfunction in 3D

Extends mathematical understanding of fractional Laplace eigenfunctions

Provides groundwork for further spectral analysis in higher dimensions

Abstract

In this work we extend a recent result by Dyda et. al. [B. Dyda, A. Kuznetsov, M. Kwasnicki, Eigenvalues of the fractional Laplace equation in the unit ball, J. Lond. Math. Soc. (2) 95 (2017), 500-518.] to dimension 3.