Inserted: 22 jun 2004
Last Updated: 8 jan 2007
Journal: Journal of Convex Analysis
Available on line
We extend the principle of comparison with cones introduceby Crandall, Evans and Gariepy in 12 for the minimizing Lipschitz extension problem to a wide class of supremal functionals. This gives a geometrical characterization of the absolute minimizers (optimal solutions whose minimality is local). Some application to the stability of absolute minimizers with respect to the Gamma-convergence is given. A variation fo the basic idea allows to characterize the minimal Lipschitz extensions in lenght metric spaces.
Keywords: Supremal functionals, absolute minimizers, comparison with cones, minimal Lipschitz extensions