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Solutions of some partial differential equations with variable coefficients by properties of monogenic functions

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Abstract

We study some partial differential equations, by using the properties of Gateaux differen-tiable functions on a commutative algebra. It is proved that components of differentiable functions satisfy some partial differential equations with coefficients related to properties of the bases of subspaces of the corresponding algebra.

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Authors and Affiliations

  1. Department of Mathematical Analysis, Ivan Franko Zhytomyr State University, Zhytomyr, Ukraine

    Anatoliy Pogorui

  2. Tecnológico de Monterrey, Monterrey, México

    Ramón M. Rodríguez-Dagnino

Authors
  1. Anatoliy Pogorui
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  2. Ramón M. Rodríguez-Dagnino
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Correspondence to Anatoliy Pogorui.

Additional information

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 13, No. 1, pp. 118–128, January–March, 2016.

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Pogorui, A., Rodríguez-Dagnino, R.M. Solutions of some partial differential equations with variable coefficients by properties of monogenic functions. J Math Sci 220, 624–632 (2017). https://doi.org/10.1007/s10958-016-3205-3

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  • DOI: https://doi.org/10.1007/s10958-016-3205-3

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