Dirichlet Type Problem for 2D Quaternionic Time-Harmonic Maxwell System in Fractal Domains. (31st January 2020)

• Record Type: Journal Article
• Authors: Pérez, Yudier Peña; Blaya, Ricardo Abreu; Bosch, Paul; Reyes, Juan Bory
• Other Names: Li Ping Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2020(2020)
• Publication Date: 2020-01-31
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2020/4735357
• Languages: English
• ISSNs: 1687-9120

Abstract

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 R 2 . 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.