Boundary value problems for hyperholomorphic solutions of two dimensional Helmholtz equation in a fractal domain

被引：5
|
作者：
Abreu Blaya, Ricardo [1 ]
Bory Reyes, Juan [2 ]
Rodriguez Dagnino, Ramon M. [3 ]
机构：
[1] Univ Holguin, Fac Informat & Matemat, Holguin 80100, Cuba
[2] Univ Oriente, Santiago De Cuba, Cuba
[3] Tecnol Monterrey, Dept Ingn Elect & Computac, Monterrey 64849, NL, Mexico
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2015年 / 261卷
关键词：
Quaternionic analysis; Helmholtz equations; Boundary value problems; Fractral geometry; MAXWELLS EQUATIONS; OPERATORS;
D O I：
10.1016/j.amc.2015.03.103
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A theory of quaternion-valued functions, called hyperholomorphic, of two real variables has long been established. This theory is in the same relation to the two dimensional Helmholtz equation as the usual one-dimensional complex analysis is to the Laplace equation in R-2. In this work we define a new Cauchy integral for domains with fractal boundary illustrating its applications and usage to study the jump and Dirichlet type boundary value problems in a fractal domain. (C) 2015 Elsevier Inc. All rights reserved.
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页码：183 / 191
页数：9
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