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 \({\mathbb{R}}^n\), the solution of viscosity of equation \(\Delta_\infty (u) = 0\) with Dirichlet’s condition.
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Le Gruyer, E. On absolutely minimizing lipschitz extensions and PDE \(\Delta_\infty (u) = 0\) . Nonlinear differ. equ. appl. 14, 29–55 (2007). https://doi.org/10.1007/s00030-006-4030-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00030-006-4030-z