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

Rosa Barbato; Francesca de Giovanni; Alba Lia Masiello

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arXiv · 2504.01715

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

Rosa Barbato·Francesca de Giovanni·Alba Lia Masiello

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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.

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Rosa Barbato, Francesca de Giovanni, Alba Lia Masiello. 2025-04-02. The asymptotic behavior of the first Robin eigenvalue with negative parameter as $p$ goes to $+\infty$. https://arxiv.org/abs/2504.01715

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