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2005•Bulletin of the London Mathematical SocietyRequires access

THE GAUSS–GREEN THEOREM IN THE CONTEXT OF LEBESGUE INTEGRATION

Washek F. Pfeffer

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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. 2000 Mathematics Subject Classification 28A15 (primary), 26A45 (secondary).

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What this paper is about

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. 2000 Mathematics Subject Classification 28A15 (primary), 26A45 (secondary).

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Available 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. 2000 Mathematics Subject Classification 28A15 (primary), 26A45 (secondary).

Key concepts: Mathematics, Divergence theorem, Lebesgue integration, Gauss, Laplace transform, Context (archaeology), Bounded function, Divergence (linguistics)

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