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Some boundary value problems are solved for time-harmonic electromagnetic fields on fractal domains, in the framework of exploiting hypercomplex function theory. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Let Ω be a bounded open and oriented connected subset of ℝ which has a compact topological boundary Γ, let C be the Dirac operator in ℝ, and let ℝ be the Clifford algebra constructed over the quadratic space ℝ. An ℝ-valued smooth function f : Ω → ℝ in Ω is called monogenic in Ω if Df = 0 in Ω. The aim of this paper is to present the most general condition on Γ obtained so far for which a Hölder continuous function f can be decomposed as F − F = f on Γ, where the components F are extendable to monogenic functions in Ω with Ω := Ω, and Ω := ℝ \ (Ω ⋃ Γ), respectively. [ABSTRACT FROM AUTHOR]