The \infty eigenvalue problem and a problem of optimal transportation

zbMATH Open1189.35214arXiv0811.1934MaRDI QIDQ3400214

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Publication date: 5 February 2010

Abstract: The so-called eigenvalues and eigenfunctions of the infinite Laplacian $Delt{a}_{i}nfty$ are defined through an asymptotic study of that of the usual $p$-Laplacian $Delt{a}_p$, 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.

Full work available at URL: https://arxiv.org/abs/0811.1934

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