Carlo Nitsch

On the solutions to p-Poisson equation with Robin boundary conditions when p goes to +∞

We study the behaviour when p → +∞, 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 ∞-Laplacian. Moreover, in the second part of the article, we focus our attention on the p-Poisson equation when the datum f belongs to L∞(Ω) and we study the behaviour of solutions when p → ∞.