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.
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页码：743 / 749
页数：7
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