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arXiv · 1206.0624

Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates

Augusto C. Ponce
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Abstract

We prove that every closed set which is not sigma-finite with respect to the Hausdorff measure H^{N-1} carries singularities of continuous vector fields in the Euclidean space R^N for the divergence operator. We also show that finite measures which do not charge sets of sigma-finite Hausdorff measure H^{N-1} can be written as an L^1 perturbation of the divergence of a continuous vector field. The main tool is a property of approximation of measures in terms of the Hausdorff content.

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Augusto C. Ponce. 2012-09-11. Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates. https://doi.org/10.1512/iumj.2013.62.5079

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