On the second eigenvalue of the infinity Laplacian with Robin boundary conditions

2024/10/17 by Vincenzo Amato, Amato, Vincenzo, Alba Lia Masiello +5
Computer Science · Mathematics · #35J92 #35J94 #35P15 #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.2410.13356

openalex publication_date 2024/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the behaviour, as p → +∞, of the second eigenvalues of the p-Laplacian with Robin boundary conditions and the limit of the associated eigenfunctions. We prove that, up to some regularity of the set, the limit of the second eigenvalues is actually the second eigenvalue of the so-called ∞-Laplacian.

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