Dirichlet Type Problem for 2D Quaternionic Time-Harmonic Maxwell System in Fractal Domains

Abstract

We investigate an electromagnetic Dirichlet type problem for the 2D quaternionic time-harmonic Maxwell system over a great generality of fractal closed type curves, which bound Jordan domains in R2. The study deals with a novel approach of h-summability condition for the curves, which would be extremely irregular and deserve to be considered fractals. Our technique of proofs is based on the intimate relations between solutions of time-harmonic Maxwell system and those of the Dirac equation through some nonlinear equations, when both cases are reformulated in quaternionic forms.