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

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.