# On the structure of divergence-free measures on $\mathbb R^2$

created by bonicatto on 23 Dec 2019

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Submitted Paper

Inserted: 23 dec 2019
Last Updated: 23 dec 2019

Year: 2019

Abstract:

We consider the structure of divergence-free vector measures on the plane. We show that such measures can be decomposed into measures induced by closed simple curves. We also discuss similar decompositions for some measures with nonzero divergence. As an application we generalize certain rigidity properties of divergence-free vector fields to vector-valued measures.