The so-called eigenvalues and eigenfunctions of the infinite Laplacian ∆∞ are defined through an asymptotic study of that of the usual p-Laplacian ∆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.
The infinite-eigenvalue problem and a problem of optimal transportation / CHAMPION T; DE PASCALE L; JIMENEZ C. - In: COMMUNICATIONS IN APPLIED ANALYSIS. - ISSN 1083-2564. - STAMPA. - 13:4(2009), pp. 547-565.
The infinite-eigenvalue problem and a problem of optimal transportation
DE PASCALE, LUIGI;
2009
Abstract
The so-called eigenvalues and eigenfunctions of the infinite Laplacian ∆∞ are defined through an asymptotic study of that of the usual p-Laplacian ∆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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