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

  • E. Le GruyerEmail author


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:

35J70 35B50 39B82 26A16 65N12 


infinity Laplacian harmonious extensions maximum principles viscosity solutions 

Copyright information

© Birkhäuser Verlag, Basel 2007

Authors and Affiliations

  1. 1.Institut National des Sciences AppliquéesRennes cedexFrance

Personalised recommendations