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

Abstract:

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 R². 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.

Año de publicación:

2015

Keywords:

• Boundary value problems
• Quaternionic analysis
• fractal geometry
• Helmholtz equations

Fuente:

scopus