The asymptotic behavior of the first Robin eigenvalue with negative parameter as $p$ goes to $+\infty$

In this paper, we want to study the asymptotic behavior of the first $p$-Laplacian eigenvalue, with Robin boundary conditions, with negative boundary parameter. In particular, we prove that the limit of the eigenfunctions is a viscosity solution for the infinity Laplacian eigenvalue problem.

Publication Details

Journal
ArXiv.org
Published
2025-04-02
Primary Topic
Nonlinear Partial Differential Equations
Type
article
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article

The asymptotic behavior of the first Robin eigenvalue with negative parameter as $p$ goes to $+\infty$

ArXiv.org
Nonlinear Partial Differential Equations
article

The asymptotic behavior of the first Robin eigenvalue with negative parameter as $p$ goes to $+\infty$

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Abstract

In this paper, we want to study the asymptotic behavior of the first $p$-Laplacian eigenvalue, with Robin boundary conditions, with negative boundary parameter. In particular, we prove that the limit of the eigenfunctions is a viscosity solution for the infinity Laplacian eigenvalue problem.

ArXiv.org
Openalex Percentile: Top 38%
Nonlinear Partial Differential Equations
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The asymptotic behavior of the first Robin eigenvalue with negative parameter as $p$ goes to $+\infty$ · ArXiv.org (2025) | TGRS Research Map | TGRS