abstract
- © 2015, Sociedade Brasileira de Matemática. The aim of this paper is to offer a new definition of Cauchy integral associated with Maxwell equations on 3-dimensional domains with fractal boundaries. This new Cauchy integral leads to several types of integral representation formulas, including the Cauchy representation formula for time-harmonic electromagnetic fields. Our approach is based on the framework of exploiting the close and well-defined connection between the quaternionic analysis and Maxwell equations.