2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173958The so-called eigenvalues and eigenfunctions of the infinite Laplacian $Δ_\infty$ are defined through an asymptotic study of that of the usual $p$-Laplacian $Δ_p$, this brings to a characterization via a non-linear eigenvalue problem for a PDE satisfied in the viscosity sense. In this paper, we obtain an other characterization of the first eigenvalue via a problem of optimal transportation, and recover properties of the first eigenvalue and corresponding positive eigenfunctions.Optimization and Controltext