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THE GAUSS–GREEN THEOREM IN THE CONTEXT OF LEBESGUE INTEGRATION

Published online by Cambridge University Press:  08 February 2005

WASHEK F. PFEFFER
WASHEK F. PFEFFER
Affiliation:
Department of Mathematics, University of California, Davis, CA 95616, USAwfpfeffer@ucdavis.edu
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Abstract

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.

Keywords

28A15 (primary)26A45 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 1 , January 2005 , pp. 81 - 94
Copyright
© The London Mathematical Society 2005

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