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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The divergence theorem for unbounded vector fields


Authors: Thierry De Pauw and Washek F. Pfeffer
Journal: Trans. Amer. Math. Soc. 359 (2007), 5915-5929
MSC (2000): Primary 26B20; Secondary 26B05, 28A75
Published electronically: July 23, 2007
MathSciNet review: 2336310
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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.


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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
Email: wfpfeffer@ucdavis.edu; washek@mcn.org

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04178-5
PII: S 0002-9947(07)04178-5
Keywords: BV sets, Hausdorff measures, Minkowski contents
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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.