The \infty eigenvalue problem and a problem of optimal transportation
Optimization and Control
2008-11-13 v1
Abstract
The so-called eigenvalues and eigenfunctions of the infinite Laplacian are defined through an asymptotic study of that of the usual -Laplacian , 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
Cite
@article{arxiv.0811.1934,
title = {The \infty eigenvalue problem and a problem of optimal transportation},
author = {Thierry Champion and Luigi De Pascale and Chloé Jimenez},
journal= {arXiv preprint arXiv:0811.1934},
year = {2008}
}