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The divergence theorem for unbounded vector fields
Author(s):
Thierry
De Pauw;
Washek
F.
Pfeffer
Journal:
Trans. Amer. Math. Soc.
359
(2007),
5915-5929.
MSC (2000):
Primary 26B20;
Secondary 26B05, 28A75
Posted:
July 23, 2007
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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:
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
Posted:
July 23, 2007
Additional Notes:
The first author was a {\em chercheur qualifié\/} of the {\em Fonds National de la Recherche Scientifique\/} in Belgium
The second author was supported in part by the {\em Université Catholique de Louvain\/} in Belgium
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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