The divergence theorem for unbounded vector fields
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- by Thierry De Pauw and Washek F. Pfeffer PDF
- Trans. Amer. Math. Soc. 359 (2007), 5915-5929 Request permission
Abstract:
In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector fields that can have singularities at every point of a compact set whose Minkowski content of codimension greater than two is finite. The resulting integration by parts theorem is applied to removable sets of holomorphic and harmonic functions.References
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Additional Information
- Thierry De Pauw
- Affiliation: Département de mathématiques, Université Catholique de Louvain, 2 chemin du cyclotron, B-1348 Louvain-la-Neuve, Belgium
- Email: depauw@math.ucl.ac.be
- Washek F. Pfeffer
- Affiliation: Department of Mathematics, University of California, Davis, California 95616
- MR Author ID: 138980
- Email: wfpfeffer@ucdavis.edu; washek@mcn.org
- Received by editor(s): August 11, 2005
- Published electronically: July 23, 2007
- Additional Notes: The first author was a chercheur qualifié of the Fonds National de la Recherche Scientifique in Belgium
The second author was supported in part by the Université Catholique de Louvain in Belgium - © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 5915-5929
- MSC (2000): Primary 26B20; Secondary 26B05, 28A75
- DOI: https://doi.org/10.1090/S0002-9947-07-04178-5
- MathSciNet review: 2336310