On the solutions to $p$-Poisson equation with Robin boundary conditions when $p$ goes to $+\infty$

Vincenzo Amato; Alba Lia Masiello; Carlo Nitsch; Cristina Trombetti

On the solutions to $p$-Poisson equation with Robin boundary conditions when $p$ goes to $+\infty$

Analysis of PDEs 2024-01-09 v3

Authors: Vincenzo Amato , Alba Lia Masiello , Carlo Nitsch , Cristina Trombetti

Abstract

We study the behaviour, when $p \to +\infty$ , of the first $p$ -Laplacian eigenvalues with Robin boundary conditions and the limit of the associated eigenfunctions. We prove that the limit of the eigenfunctions is a viscosity solution to an eigenvalue problem for the so-called $\infty$ -Laplacian.

Keywords

p-Laplacian Robin boundary conditions eigenvalue problem infinity-Laplacian viscosity solution asymptotic behavior

Cite

@article{arxiv.2111.10107,
  title  = {On the solutions to $p$-Poisson equation with Robin boundary conditions when $p$ goes to $+\infty$},
  author = {Vincenzo Amato and Alba Lia Masiello and Carlo Nitsch and Cristina Trombetti},
  journal= {arXiv preprint arXiv:2111.10107},
  year   = {2024}
}

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