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Principal eigenvalue problem for infinity Laplacian in metric spaces
Abstract This article is concerned with the Dirichlet eigenvalue problem associated with the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>∞</m:mi> </m:math> \infty -Laplacian in metric spaces. We establish a direct partial differential equation approach to find the principal eigenvalue and eigenfunctions in a proper geodesic space without assuming any measure structure. We provide an …