partial derivative-problem in domains of C2 in terms of hyper-conjugate harmonic functions

被引：5

作者：

Abreu-Blaya, Ricardo ^{[2
]}

Bory-Reyes, Juan ^{[3
]}

Elena Luna-Elizarraras, Maria ^{[1
]}

Shapiro, Michael ^{[1
]}

机构：

[1] IPN, Escuela Super Fis & Matemat, Mexico City 07738, DF, Mexico

[2] Univ Holguin, Dept Matemat, Holguin 80100, Cuba

[3] Univ Oriente, Dept Matemat, Santiago De Cuba 90500, Cuba

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2012年 / 57卷 / 7-8期

关键词：

partial derivative-problem; Cauchy-Fueter operator; Borel-Pompeiu formula; Theodoresco operator; hyper-conjugate harmonic functions;

D O I：

10.1080/17476933.2011.598933

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a Jordan domain of C-2, we consider the partial derivative-problem and establish a necessary and sufficient condition for its solvability in terms of the existence of hyper-conjugate harmonic functions, a notion coming from quaternionic analysis. Besides, whenever the partial derivative-problem is solvable we give its general solution in a quite explicit form.

引用

页码：743 / 749

页数：7

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