Removable singularities for the equation div v = 0

Moonens, Laurent
(2006) 30th Summer Symposium in Real Analysis — Location: Asheville, NC, USA (13.June.2006)

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  • Moonens, LaurentUCLouvain
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Abstract
A compact subset S of R^N is removable for the equation div v = 0 if every bounded Borel vector field whose distributional divergence vanishes outside S, has a zero distributional divergence in the whole R^N. Here we establish that a compact subset of R^N is removable for the equation div v = 0 if and only if its (N−1)-dimensional Hausdorff measure vanishes.
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Moonens, L. (2006). Removable singularities for the equation div v = 0. Real Analysis Exchange, 30th Summer Symposium Conference, 125-132. https://hdl.handle.net/2078.5/159700 (Original work published 2006)