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28a15 (primary)

Bulletin of the London Mathematical Society (1)

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THE GAUSS–GREEN THEOREM IN THE CONTEXT OF LEBESGUE INTEGRATION
WASHEK F. PFEFFER
Journal:

Bulletin of the London Mathematical Society / Volume 37 / Issue 1 / January 2005

Published online by Cambridge University Press:

08 February 2005, pp. 81-94

Print publication:

January 2005
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In the context of Lebesgue integration the Gauss–Green theorem is proved for bounded vector fields with substantial sets of singularities with respect to continuity and differentiability. The resulting integration by parts is applied to removable sets for the Cauchy–Riemann, Laplace, and minimal surface equations. A simple connection between the Gauss–Green theorem and distributional divergence is established.