Some Riemann boundary value problems in Clifford analysis (I)

In this article, we first give the Plemelj formula for functions with parameter by following the classical method. Then by using the higher order Cauchy integral representation formulas, some properties for harmonic functions and bi-harmonic functions are presented, for example, the mean value theor...

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Bibliographic Details
Published in:	Complex variables and elliptic equations Vol. 58; no. 7; pp. 991 - 1003
Main Authors:	Zhang, Zhongxiang, Gürlebeck, Klaus
Format:	Journal Article
Language:	English
Published:	Colchester Taylor & Francis Group 01-07-2013 Taylor & Francis Ltd
Subjects:	bi-harmonic function Boundary value problems Complex variables Harmonic functions Integrals Mathematical analysis Plemelj formula Representations Riemann boundary value problem Theorems
Online Access:	Get full text
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Summary:	In this article, we first give the Plemelj formula for functions with parameter by following the classical method. Then by using the higher order Cauchy integral representation formulas, some properties for harmonic functions and bi-harmonic functions are presented, for example, the mean value theorem, the Painlevé theorem, etc. Finally, we consider the Riemann boundary value problems for harmonic functions and bi-harmonic functions in Clifford analysis, the solutions are given in an explicit way.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	1747-6933 1747-6941
DOI:	10.1080/17476933.2011.613119