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

Yudier Peña-Pérez, Ricardo Abreu-Blaya, Juan Bory-Reyes, Baruch Schneider

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number189
JournalJournal of Geometric Analysis
Issue number7
StatePublished - Jul 2022


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


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