Schwarz problem in lens and lune

被引：32
作者：
Begehr, H. [1 ]
Vaitekhovich, T. [2 ]
机构：
[1] FU Berlin, Math Inst, D-14195 Berlin, Germany
[2] Univ Bonn, Inst Med Biom, D-53105 Bonn, Germany
来源：
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2014年 / 59卷 / 01期
关键词：
Schwarz problem; Cauchy-Riemann equation; Schwarz kernel; Poisson kernel; lens; lune; BOUNDARY-VALUE-PROBLEMS; CAUCHY-RIEMANN EQUATION; GREEN-FUNCTIONS; REFLECTIONS;
D O I：
10.1080/17476933.2013.799152
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Schwarz problem is explicitly solved for the inhomogeneous Cauchy-Riemann equation in a particular circular lens and two related complementary lunes. The solutions are given by the same analytical formula restricted to the respective domain. The parqueting-reflection method is used to construct the Cauchy-Schwarz representation formula leading to the Schwarz and thus the Poisson kernels for the three domains.
引用
收藏
页码：76 / 84
页数：9
相关论文
共 20 条
[1]  
Abdymanapov S. A., 2005, MOR PROGR AN P 5 INT, P1137
[2]  
Abdymanapov SA., 2005, EURASIAN MATH J, V3, P22
[3]   Two basic boundary-value problems for the inhomogeneous Cauchy-Riemann equation in an infinite sector [J].
Akel, Mohamed S. ;
Hussein, Hussein S. .
ADVANCES IN PURE AND APPLIED MATHEMATICS, 2012, 3 (03) :315-328
[4]  
Begehr H, 2011, EURASIAN MATH J, V2, P139
[5]   Harmonic Dirichlet problem for some equilateral triangle [J].
Begehr, H. ;
Vaitekhovich, T. .
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2012, 57 (2-4) :185-196
[6]  
Begehr H, 2010, EURASIAN MATH J, V1, P17
[7]   How to find harmonic Green functions in the plane [J].
Begehr, H. ;
Vaitekhovich, T. .
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2011, 56 (12) :1169-1181
[8]  
Begehr H., 1994, COMPLEX ANAL METHODS
[9]  
Begehr H., 2008, UZBEK MATH J, V4, P29
[10]  
Begehr H, 2007, ACAD SCI, V1, P119
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