Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates
(2013) Indiana University Mathematics Journal — Vol. 62, n° 4, p. 1055-1074 (2013)
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- Abstract
- We prove that every closed set which is not (sigma)-finite with respect to the Hausdorff measure (cH^{N-1}) carries singularities of continuous vector fields in (R^N) for the divergence operator. We also show that finite measures which do not charge sets of (sigma)-finite Hausdorff measure (cH^{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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Ponce, A. (2013). Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates. Indiana University Mathematics Journal, 62(4), 1055-1074. https://doi.org/10.1512/iumj.2013.62.5079 (Original work published 2013)