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Electromagnetic Riemann–Hilbert Boundary Value Problem in Fractal Domains of \({\mathbb R}^2\)

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Abstract

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 \({\mathbb R}^2\) 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.

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Funding

Partial financial support was received from Instituto Politécnico Nacional (grant number SIP20211188) and Postgraduate Study Fellowship of the Consejo Nacional de Ciencia y Tecnología (CONACYT) (Grant Number 744134).

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Authors and Affiliations

  1. Facultad de Matemáticas, Universidad Autonóma de Guerrero, Chilpancingo, México

    Yudier Peña-Pérez & Ricardo Abreu-Blaya

  2. ESIME-Zacatenco, Instituto Politécnico Nacional, Ciudad de México, México

    Juan Bory-Reyes

  3. Department of Mathematics, Faculty of Science, University of Ostrava, Ostrava, Czechia

    Baruch Schneider

Authors
  1. Yudier Peña-Pérez
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  2. Ricardo Abreu-Blaya
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  3. Juan Bory-Reyes
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  4. Baruch Schneider
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The authors contributed equally in this paper and typed, read, and approved the final form of the manuscript.

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Correspondence to Baruch Schneider.

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Peña-Pérez, Y., Abreu-Blaya, R., Bory-Reyes, J. et al. Electromagnetic Riemann–Hilbert Boundary Value Problem in Fractal Domains of \({\mathbb R}^2\). J Geom Anal 32, 189 (2022). https://doi.org/10.1007/s12220-022-00929-9

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  • DOI: https://doi.org/10.1007/s12220-022-00929-9

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