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

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