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

TL;DR

This paper reviews known properties of the subdifferential for one-homogeneous functionals, such as anisotropic total variation variants, and introduces a new link between Lebesgue points of calibrating fields and regular points of level lines.

Contribution

It establishes a novel relationship connecting Lebesgue points of calibrating fields with regular points of level lines for these functionals.

Findings

Connection between Lebesgue points and regular points of level lines.

Extension of properties of anisotropic, nonhomogeneous total variation.

Enhanced understanding of subdifferential structure for one-homogeneous functionals.

Abstract

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.