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

摘要

We collect some known results on the subdifferentials of a class of one-homogeneous functionals, which consist in anisotropic and nonhomogeneous variants of the total variation. It is known that the subdifferential at a point is the divergence of some "calibrating field". We establish new relationships between Lebesgue points of a calibrating field and regular points of the level surfaces of the corresponding calibrated function.