## The \infty eigenvalue problem and a problem of optimal transportation

##### Authors
Champion, Thierry
De Pascale, Luigi
Jimenez, Chloé
##### Description
The so-called eigenvalues and eigenfunctions of the infinite Laplacian $\Delta_\infty$ are defined through an asymptotic study of that of the usual $p$-Laplacian $\Delta_p$, 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.
##### Keywords
Mathematics - Optimization and Control