A pointwise characterization of the subdifferential of the total   variation functional
  We derive a new pointwise characterization of the subdifferential of the total variation (TV) functional. It involves a full trace operator which maps certain $ L^q $ - 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. 
K. Bredies and M. Holler
math.FA