Title: Rigidity and trace properties of divergence-measure vector fields,
Abstract: We show some rigidity properties of divergence-free vector fields defined on
half-spaces. As an application, we prove the existence of the classical trace
for a bounded, divergence-measure vector field $\xi$ defined on the Euclidean
plane, at almost every point of a locally oriented rectifiable set $S$, under
the assumption that its weak normal trace $[\xi\cdot \nu_S]$ attains a local
maximum for the norm of $\xi$ at the point.