The \infty eigenvalue problem and a problem of optimal transportation

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

2008-11-12

arxiv.org/abs/0811.1934v1

Mathematics

Optimization and Control

Scientific paper

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.

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