The divergence theorem for unbounded vector fields

De Pauw, Thierry; Pfeffer, Washek

doi:10.1090/S0002-9947-07-04178-5

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.

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