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Schwarz boundary-value problems for solutions of a generalized Cauchy–Riemann system with a singular line

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Abstract

We consider a generalized Cauchy–Riemann system with a rectilinear singular interval of the real axis. Schwarz boundary value problems for generalized analytic functions which satisfy the mentioned system are reduced to the Fredholm integral equations of the second kind under natural assumptions relating to the boundary of a domain and the given boundary functions.

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Authors and Affiliations

  1. Institute of Mathematics of the National Academy of Science of Ukraine, Kyiv, Ukraine

    Sergiy A. Plaksa

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  1. Sergiy A. Plaksa
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Correspondence to Sergiy A. Plaksa.

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Dedicated to the memory of Professor Bogdan Bojarski

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 16, No. 2, pp. 200–214 April–June, 2019.

This research is partially supported by the State Program of Ukraine (Project No. 0117U004077).

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Plaksa, S.A. Schwarz boundary-value problems for solutions of a generalized Cauchy–Riemann system with a singular line. J Math Sci 244, 36–46 (2020). https://doi.org/10.1007/s10958-019-04602-5

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  • DOI: https://doi.org/10.1007/s10958-019-04602-5

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