On Absolutely Minimizing Lipschitz Extensions and PDE Δ_infty = 0

2004/03/09 by Erwan Le Gruyer, Gruyer, Erwan Le · 1 citation
Mathematics · #35B50 #35J60 #35J70 #65D05 #65N12 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:35B50 #msc:35J60 #msc:35J70 #msc:65D05 #msc:65N12

paper · pdf · doi:10.48550/arxiv.math/0403158

2004-02

arxiv created 2004/03/09 · arxiv updated 2009/12/01

Abstract

We prove the existence of Absolutely Minimizing Lipschitz Extensions by a method which differs from those used by G. Aronsson in general metrically convex compact metric spaces and R. Jensen in Euclidean spaces. Assuming Jensen's hypotheses, our method yields numerical schemes for computing, in euclidean \mathbb R, the solution of viscosity of equation Δ_∞=0 with Dirichlet's condition.

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