Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates
Analysis of PDEs
2014-07-07 v2 Metric Geometry
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.
Keywords
Cite
@article{arxiv.1206.0624,
title = {Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates},
author = {Augusto C. Ponce},
journal= {arXiv preprint arXiv:1206.0624},
year = {2014}
}