In this paper we present a hyperholomorphic (associated to the Helmholtz equation) approach to the Riemann–Hilbert boundary value problem (RHBVP for short) in domains of R2 with h- summable boundaries. We apply our results to Maxwell’s system and study an electromagnetic RHBVP for the case time-harmonic. The study is based on a reformulation of the time-harmonic Maxwell system in terms of electromagnetic potentials. The main geometric ingredient is the h- summability condition assumed for domains’ boundaries, which are considered fractals.
- Fractal curves
- Maxwell system
- Riemann–Hilbert boundary value problem