Removable Sets for the Flux of Continuous Vector Fields
(2010) Proceedings of the American Mathematical Society — Vol. 138, n° 2, p. 655-661 (2010)
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- Abstract
- We show that any closed set E having a sigma-finite (n - 1)-dimensional Hausdorff measure does not support the nonzero distributional divergence of a continuous vector field; in particular it has the property that any C-1 function in R-n that is harmonic outside it is harmonic in R-n. We also exhibit a compact set E having Hausdorff dimension n - 1, supporting the nonzero distributional divergence of a continuous vector field yet having the property that any C-1 function that is harmonic outside E is harmonic in R-n.
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de Valeriola, S., & Moonens, L. (2010). Removable Sets for the Flux of Continuous Vector Fields. Proceedings of the American Mathematical Society, 138(2), 655-661. https://doi.org/10.1090/S0002-9939-09-10092-8 (Original work published 2010)