On the divergence theorem on manifolds

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:397

Article

Boonpogkrong, Varayu^2,3  Chew, Tuan Seng¹  Lee, Peng Yee⁴ 

[1] Natl Univ Singapore, Fac Sci, Dept Math, Singapore 119076, Singapore

[2] Prince Songkla Univ, Fac Sci, Dept Math & Stat, Hat Yai 90112, Thailand

[3] CHE, Ctr Excellence Math, Bangkok 10400, Thailand

[4] Nanyang Technol Univ, Natl Inst Educ, Singapore 637616, Singapore

关键词: The H-K integral;    Partition of unity;    Manifolds;    The divergence theorem;   

DOI  :  10.1016/j.jmaa.2012.07.042

来源: Elsevier

【 摘 要 】

In this paper, the divergence theorem is proved by the Kurzweil-Henstock approach. The physical definition of the divergence of a vector field is used, instead of the usual definition used in mathematics papers. Sufficient conditions for the existence of the divergence of a vector field on n-dimensional manifolds in R-n are given. Concepts of strong differentiability are used in the sufficient conditions. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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