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

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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 
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/
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     author = {T. Champion and L. De Pascale},
     title = {Principles of {Comparison} with {Distance} {Functions} for {Absolute} {Minimizers}},
     journal = {Journal of convex analysis},
     pages = {515--541},
     year = {2007},
     volume = {14},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a3/}
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