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The Gauss–Green Theorem in the Context of Lebesgue Integration
Author(s) -
Pfeffer W. F.
Publication year - 2005
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609304003777
Subject(s) - mathematics , divergence theorem , lebesgue integration , gauss , laplace transform , context (archaeology) , bounded function , divergence (linguistics) , mathematical analysis , pure mathematics , fundamental theorem of calculus , integration by parts , cauchy distribution , lebesgue's number lemma , green's theorem , picard–lindelöf theorem , riemann integral , singular integral , integral equation , paleontology , linguistics , philosophy , physics , quantum mechanics , fixed point theorem , biology
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).