Electromagnetic Riemann–Hilbert Boundary Value Problem in Fractal Domains of R²

Abstract:

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.

Año de publicación:

2022

Keywords:

• Fractal curves
• Riemann–Hilbert boundary value problem
• Maxwell system

Fuente:

scopus