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Dirichlet Problem for a Generalized Cauchy–Riemann Equation with a Supersingular Point on a Half-Plane

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Abstract

For equations with a Cauchy–Riemann operator involving a strong point singularity in the lower coefficient on a half-plane, an integral representation of the solution is obtained in the class of bounded functions and a Dirichlet-type problem is studied. The calculation of the Vekua–Pompeiu integral is examined in the case when the density of the integral has strong singularities in a set of points or lines.

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Authors and Affiliations

  1. National Research University “Moscow Power Engineering Institute”, 111250, Moscow, Russia

    I. N. Dorofeeva & A. B. Rasulov

Authors
  1. I. N. Dorofeeva
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  2. A. B. Rasulov
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Correspondence to I. N. Dorofeeva or A. B. Rasulov.

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Translated by N. Berestova

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Dorofeeva, I.N., Rasulov, A.B. Dirichlet Problem for a Generalized Cauchy–Riemann Equation with a Supersingular Point on a Half-Plane. Comput. Math. and Math. Phys. 60, 1679–1685 (2020). https://doi.org/10.1134/S0965542520100073

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  • DOI: https://doi.org/10.1134/S0965542520100073

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