On absolutely minimizing lipschitz extensions and PDE \(\Delta_\infty (u) = 0\)


DOI: 10.1007/s00030-006-4030-z

Cite this article as:
Le Gruyer, E. Nonlinear differ. equ. appl. (2007) 14: 29. doi:10.1007/s00030-006-4030-z


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 \({\mathbb{R}}^n\), the solution of viscosity of equation \(\Delta_\infty (u) = 0\) with Dirichlet’s condition.

2000 Mathematics Subject Classification:



infinity Laplacianharmonious extensionsmaximum principlesviscosity solutions
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© Birkhäuser Verlag, Basel 2007

Authors and Affiliations

  1. 1.Institut National des Sciences AppliquéesRennes cedexFrance