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.

引用

页码：183 / 191

页数：9

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