English

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 Δ\Delta_\infty are defined through an asymptotic study of that of the usual pp-Laplacian Δp\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

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}
}
R2 v1 2026-06-21T11:40:49.548Z