On the structure of the second eigenfunctions of the p-Laplacian on a ball

2015/06/17 by T. V. Anoop, Anoop, T. V., P. Drabek +4
Computer Science · Mathematics · #35B06 #35J92 #35P30 #49R05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #msc:35B06 #msc:35J92 #msc:35P30 #msc:49R05

paper · pdf · doi:10.48550/arxiv.1506.05184

arxiv created 2015/06/17 · openalex publication_date 2015/06/17 · arxiv updated 2015/06/18 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that the second eigenfunctions of the p-Laplacian, p>1, are not radial on the unit ball in ℝ^N, for any N≥ 2. Our proof relies on the variational characterization of the second eigenvalue and a variant of the deformation lemma. We also construct an infinite sequence of eigenpairs \τ_n,Ψ_n\ such that Ψ_n is nonradial and has exactly 2n nodal domains. A few related open problems are also stated.

Citations

• Boundary regularity for solutions of degenerate elliptic equations

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