Nonradiality of second fractional eigenfunctions of thin annuli

2022/01/13 by Sidy Moctar Djitte, Djitte, Sidy M., Sven Jarohs +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2201.04907

openalex publication_date 2022/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we study properties of the second Dirichlet eigenvalue of the fractional Laplacian of annuli-like domains and the corresponding eigenfunctions. In the first part, we consider an annulus with inner radius R and outer radius R+1. We show that for R sufficiently large any corresponding second eigenfunction of this annulus is nonradial. In the second part, we investigate the second eigenvalue in domains of the form B₁(0)∖ B_τ(a), where a is in the unitary ball and 0<τ<1-|a|. We show that this value is maximized for a=0, if the set B₁(0)∖ B_τ(0) has no radial second eigenfunction. We emphasize that the first part of our paper implies that this assumption is indeed nonempty.

Related

• Nonradiality of second eigenfunctions of the fractional Laplacian in a ball
• On the structure of the second eigenfunctions of the p-Laplacian on a ball
• Dirichlet eigenfunction and heat kernel estimates on annular domains
• Asymptotic behavior for the radial eigenvalues of p-Laplacian in certain annular domains
• Inequalities for the minimal eigenvalue of the Laplacian in an annulus