数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (1): 235-254.doi: 10.1016/S0252-9602(14)60154-5

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THE GAUSS–GREEN THEOREM IN CLIFFORD ANALYSIS AND ITS APPLICATIONS

罗纬宇|杜金元   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2013-11-24 修回日期:2014-04-14 出版日期:2015-01-20 发布日期:2015-01-20
  • 基金资助:

    This work was supported by NNSF of China (11171260) and RFDP of Higher Education of China (20100141110054).

THE GAUSS–GREEN THEOREM IN CLIFFORD ANALYSIS AND ITS APPLICATIONS

LUO Wei Yu,DU Jin Yuan   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2013-11-24 Revised:2014-04-14 Online:2015-01-20 Published:2015-01-20
  • Supported by:

    This work was supported by NNSF of China (11171260) and RFDP of Higher Education of China (20100141110054).

摘要:

In this article, we establish the Gauss–Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very gen- eral by using the geometric measure theoretic method. The Cauchy–Pompeiu formula for Clifford-valued functions under the weak condition will be derived as their simple applica- tion. Furthermore, Cauchy formula for monogenic functions under the weak condition is derived directly from the Cauchy–Pompeiu formula.

关键词: Gauss–Green theorem, Cauchy’s theorem, Cauchy–Pompeiu formula, Clifford analysis, Geometric measure theory

Abstract:

In this article, we establish the Gauss–Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very gen- eral by using the geometric measure theoretic method. The Cauchy–Pompeiu formula for Clifford-valued functions under the weak condition will be derived as their simple applica- tion. Furthermore, Cauchy formula for monogenic functions under the weak condition is derived directly from the Cauchy–Pompeiu formula.

Key words: Gauss–Green theorem, Cauchy’s theorem, Cauchy–Pompeiu formula, Clifford analysis, Geometric measure theory

中图分类号: 

  • 30G35