THE ∞-EIGENVALUE PROBLEM AND A PROBLEM OF OPTIMAL TRANSPORTATION

TitleTHE ∞-EIGENVALUE PROBLEM AND A PROBLEM OF OPTIMAL TRANSPORTATION
Publication TypeJournal Article
Year of Publication2009
AuthorsCHAMPION, THIERRY, DE PASCALE, LUIGI, JIMENEZ, CHLOE
Volume13
Issue4
Start Page547
Pagination19
Date Published2009
ISSN1083-2564
AMS99Z00
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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