Calculus of Variations and Geometric Measure Theory
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T. Champion - L. De Pascale

A principle of comparison with distance functions for absolute minimizers

created on 22 Jun 2004
modified by depascal on 08 Jan 2007


Published Paper

Inserted: 22 jun 2004
Last Updated: 8 jan 2007

Journal: Journal of Convex Analysis
Volume: 14
Number: 3
Year: 2007

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


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