THE GAUSS–GREEN THEOREM IN CLIFFORD ANALYSIS AND ITS APPLICATIONS  

作　　者：罗纬宇 杜金元 

机构地区：[1]School of Mathematics and Statistics, Wuhan University

出　　处：《Acta Mathematica Scientia》2015年第1期235-254,共20页数学物理学报（B辑英文版）

基　　金：supported by NNSF of China(11171260);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 general 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 application. Furthermore, Cauchy formula for monogenic functions under the weak condition is derived directly from the Cauchy-Pompeiu formula.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 general 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 application. 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 

分 类 号：O174[理学—数学]