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2D Quaternionic Time-Harmonic Maxwell System in Elliptic Coordinates

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Abstract

In this paper we consider the 2D time–harmonic Maxwell equations in elliptic coordinates through certain quaternionic perturbed Dirac operator. The main goal is aimed to analyze an electromagnetic Dirichlet problem for a curvilinear polygon with rectifiable boundary in \({\mathbb{R}^2}\). In addition, we provide an integral representation formula for electromagnetic fields that resembles the classical Stratton-Chu formula. The importance of the problem for applications makes it worthy of consideration.

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Authors and Affiliations

  1. Facultad de Informática y Matemática, Universidad de Holguín, Holguín, 80100, Cuba

    Ricardo Abreu–Blaya & Rafael Ávila–Ávila

  2. Departamento de Matemática, Universidad de Oriente, Santiago de Cuba, 90500, Cuba

    Juan Bory–Reyes

  3. Departamento de Ingeniería Eléctrica y Computacional, Tecnológico de Monterrey, Monterrey, NL, México

    Ramón M. Rodríguez–Dagnino

Authors
  1. Ricardo Abreu–Blaya
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  2. Rafael Ávila–Ávila
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  3. Juan Bory–Reyes
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  4. Ramón M. Rodríguez–Dagnino
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Correspondence to Ramón M. Rodríguez–Dagnino.

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Abreu–Blaya, R., Ávila–Ávila, R., Bory–Reyes, J. et al. 2D Quaternionic Time-Harmonic Maxwell System in Elliptic Coordinates. Adv. Appl. Clifford Algebras 25, 255–270 (2015). https://doi.org/10.1007/s00006-014-0485-x

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