The \infty eigenvalue problem and a problem of optimal transportation

Thierry Champion (1) , Luigi de Pascale (2) , Chloé Jimenez (3)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134
2 Dipartimento di matematica di Pisa
3 LM - Laboratoire de mathématiques de Brest

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.

Domaines: Optimisation et contrôle [math.OC]

Thierry Champion, Luigi de Pascale, Chloé Jimenez. The \infty eigenvalue problem and a problem of optimal transportation. 2008. ⟨hal-00338218⟩