Fine properties of the subdifferential for a class of one-homogeneous functionals

Antonin Chambolle (1) , Michael Goldman (2) , Matteo Novaga (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 MPI-MiS - Max Planck Institute for Mathematics in the Sciences
3 Dipartimento di Matematica Pura e Applicata [Padova]

We collect here some known results on the subdifferential of one-homogeneous functionals, which are anisotropic and nonhomogeneous variants of the total variation and establish a new relationship between Lebesgue points of the calibrating field and regular points of the level lines of the corresponding calibrated function.

Mots clés: reduced boundary; total variation; functions with bounded variation; calibrations

Domaines: Equations aux dérivées partielles [math.AP]

Antonin Chambolle, Michael Goldman, Matteo Novaga. Fine properties of the subdifferential for a class of one-homogeneous functionals. Advances in Calculus of Variation, 2015. ⟨hal-00746958v2⟩