On the divergence theorem on manifolds

DOI10.1016/j.jmaa.2012.07.042zbMath1252.26005OpenAlexW2087602529MaRDI QIDQ713448

Varayu Boonpogkrong, Tuan Seng Chew, Peng-Yee Lee

Publication date: 29 October 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.07.042

zbMATH Keywords

manifoldsKurzweil-Henstock integralpartition of unitythe divergence theorem

Mathematics Subject Classification ID

Denjoy and Perron integrals, other special integrals (26A39) Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) (26B20)

Cites Work

• On Henstock's inner variation and strong derivatives.
• Stokes' theorem.
• Kurzweil-Henstock integration on manifolds
• The divergence theorem for discontinuous vector fields
• The missing link
• A fundamental theorem of calculus for the Kurzweil-Henstock integral in \(\mathbb{R}^m\)
• Green-Goursat theorem
• Symmetric and Strong Differentiation
• Strong Derivatives and Inverse Mappings
• A non absolutely convergent integral which admits transformation and can be used for integration on manifolds
• The fundamental theorem for the $\nu_1$-integral on more general sets and a corresponding divergence theorem with singularities
• Sets of Finite Perimeter and the Gauss-Green Theorem with Singularities
• A Modified Differentiation
• A Note on Inverse Function Theorems
• On a Related Function Theorem
• On multiplication of Perron-integrable functions
• On Green's Theorem
• The Gauss-Green theorem
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