We derive a new pointwise characterization of the subdifferential of the total variation (TV) functional. It involves a full trace operator which maps certain Lq - vectorfields to integrable functions with respect to the total variation measure of the derivative of a bounded variation function. This full trace operator extents a notion of normal trace, frequently used, for example, to characterize the total variation flow.
@article{arxiv.1609.08918,
title = {A pointwise characterization of the subdifferential of the total variation functional},
author = {K. Bredies and M. Holler},
journal= {arXiv preprint arXiv:1609.08918},
year = {2016}
}