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Cauchy representation formulas for Maxwell equations in 3-dimensional domains with fractal boundaries

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Abstract

The aim of this paper is to offer a new definition of Cauchy integral associated with Maxwell equations on 3-dimensional domains with fractal boundaries. This new Cauchy integral leads to several types of integral representation formulas, including the Cauchy representation formula for time-harmonic electromagnetic fields. Our approach is based on the framework of exploiting the close and well-defined connection between the quaternionic analysis and Maxwell equations.

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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. ESIME-Zacatenco, Instituto Politécnico Nacional, México, DF, 07738, México

    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 Juan Bory-Reyes.

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Abreu-Blaya, R., Ávila-Ávila, R., Bory-Reyes, J. et al. Cauchy representation formulas for Maxwell equations in 3-dimensional domains with fractal boundaries. Bull Braz Math Soc, New Series 46, 681–700 (2015). https://doi.org/10.1007/s00574-015-0108-8

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  • DOI: https://doi.org/10.1007/s00574-015-0108-8

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