Abstract

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.

Author information

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Thierry Champion

Lab. d'Analyse Non Linéaire Appliquée, U.F.R. des Sciences et Techniques, Université du Sud Toulon-Var, BP 20132, 83957 La Garde, France

Luigi De Pascale

Dip. di Matematica Applicata, Università di Pisa, Via Bonanno Pisano 25/B, 56126 Pisa, Italy

Keywords

  • Supremal functionals
  • absolute minimizers
  • comparison with cones
  • comparison with distance functions
  • minimal Lipschitz extensions

Mathematics Subject Classification

49K30, 65K10

References

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Suggested citation

T. Champion, L. De Pascale. “Principles of Comparison with Distance Functions for Absolute Minimizers.” Journal of Convex Analysis 14 (2007), No. 3, 515–541. https://doi.org/10.68381/jca14032

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Published by Heldermann Verlag, 2007. Rights now held by Banach Press LLC.