Geodesic
Principles of Comparison with Distance Functions for Absolute Minimizers
Journal of convex analysis, Tome 14 (2007) no. 3, pp. 515-541.

Voir la notice de l'article provenant de la source Heldermann Verlag

We extend the principle of comparison with cones introduced by M. G. Crandall, L. C. Evans and R. F. Gariepy [Calc. Var. Partial Diff. Equations 13 (2001) 123--139] 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 Γ-convergence is given. A variation of the basic idea also allows to characterize the minimal Lipschitz extensions in length metric spaces.
Classification : 49K30, 65K10
Mots-clés : Supremal functionals, absolute minimizers, comparison with cones, comparison with distance functions, minimal Lipschitz extensions 
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T. Champion; L. De Pascale. Principles of Comparison with Distance Functions for Absolute Minimizers. Journal of convex analysis, Tome 14 (2007) no. 3, pp. 515-541. http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a3/