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

Author

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  • Yudier Peña Pérez
  • Ricardo Abreu Blaya
  • Paul Bosch
  • Juan Bory Reyes

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 . The study deals with a novel approach of - 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.

Suggested Citation

  • Yudier Peña Pérez & Ricardo Abreu Blaya & Paul Bosch & Juan Bory Reyes, 2020. "Dirichlet Type Problem for 2D Quaternionic Time-Harmonic Maxwell System in Fractal Domains," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-8, January.
    • Handle: RePEc:hin:jnlamp:4735357
    DOI: 10.1155/2020/4735357
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