Calculus of Variations and Geometric Measure Theory
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G. P. Leonardi - G. Saracco

Rigidity and trace properties of divergence-measure vector fields

created by saracco on 04 Aug 2017
modified on 04 Sep 2017


Submitted Paper

Inserted: 4 aug 2017
Last Updated: 4 sep 2017

Year: 2017

ArXiv: 1708.01393 PDF


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


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