Calculus of Variations and Geometric Measure Theory

T. Champion - L. De Pascale - C. Jimenez

The $\infty$-eigenvalue problem and a problem of optimal transportation

created by depascal on 25 Mar 2009


Accepted Paper

Inserted: 25 mar 2009

Journal: Communications in Applied Analysis
Volume: (2009)
Year: 2009


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.