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A Short Note on the Local Solvability of the Quaternionic Beltrami Equation

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Abstract

In this paper we discuss the local solvability of the inhomogeneous Beltrami equations in Quaternionic Analysis. We give an example of a Beltrami equation with no distributional solution and deduce the compatibility condition. This study is closely linked to the study of Dirac operators with non-constant coefficients.

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Authors and Affiliations

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

    Juan Bory Reyes

  2. Departamento de Matemática, Universidade de Aveiro, P-3810-159, Aveiro, Portugal

    Paula Cerejeiras

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

    Alí Guzmán Adán

  4. Departamento de Matemática, Universidade de Aveiro, P-3810-159, Aveiro, Portugal

    Uwe Kähler

Authors
  1. Juan Bory Reyes
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  2. Paula Cerejeiras
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  3. Alí Guzmán Adán
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  4. Uwe Kähler
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Corresponding author

Correspondence to Uwe Kähler.

Additional information

Dedicated to Klaus Gürlebeck on the occasion of his 60th birthday

This work was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e a Tecnologia”), within project PEst-OE/MAT/UI4106/2014.

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Bory Reyes, J., Cerejeiras, P., Guzmán Adán, A. et al. A Short Note on the Local Solvability of the Quaternionic Beltrami Equation. Adv. Appl. Clifford Algebras 24, 945–953 (2014). https://doi.org/10.1007/s00006-014-0494-9

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  • DOI: https://doi.org/10.1007/s00006-014-0494-9

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