Inserted: 4 aug 2017
Last Updated: 4 sep 2017
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.
Keywords: rigidity, divergence measure vector fields, weak normal trace