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

Abstract

We study the behaviour, when p→+∞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. Moreover, in the second part of the article, we focus our attention on the p-Poisson equation when the datum ff belongs to L∞(Ω){L}^{\infty }\left(\Omega ) and we study the behaviour of solutions when p→∞p\to \infty .

Keywords

• p-laplacian
• robin boundary conditions
• eigenvalue problem
• infinity laplacian
• 35j92
• 35j94
• 35p15