  We investigate uniqueness issues for a continuity equation arising out of the
simplest model for plasticity, Hencky plasticity. The associated system is of
the form $\rm{ curl\;}(\mu\sigma)=0$ where $\mu$ is a nonnegative measure and
$\sigma$ a two-dimensional divergence free unit vector field. After
establishing the Sobolev regularity of that field, we provide a precise
description of all possible geometries of the characteristic flow, as well as
of the associated solutions.
