THE GAUSS–GREEN THEOREM IN CLIFFORD ANALYSIS AND ITS APPLICATIONS

doi:10.1016/S0252-9602(14)60154-5

Abstract

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

CLC Number:

30G35

LUO Wei Yu,DU Jin Yuan. THE GAUSS–GREEN THEOREM IN CLIFFORD ANALYSIS AND ITS APPLICATIONS[J].Acta mathematica scientia,Series B, 2015, 35(1): 235-254.

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