# Rigidity and trace properties of divergence-measure vector fields

created by saracco on 04 Aug 2017

[BibTeX]

Preprint

Inserted: 4 aug 2017
Last Updated: 4 aug 2017

Year: 2017

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.