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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 10, Pages 1734–1740 (Mi zvmmf11147)  

Partial Differential Equations

Dirichlet problem for a generalized Cauchy–Riemann equation with a supersingular point on a half-plane

I. N. Dorofeeva, A. B. Rasulov

National Research University "Moscow Power Engineering Institute", Moscow, 111250 Russia

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.

Key words: Cauchy–Riemann operator, singular point, Vekua–Pompeiu operator, half-plane, Dirichlet- type problem.

DOI: https://doi.org/10.31857/S0044466920100075


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:10, 1679–1685

Bibliographic databases:

UDC: 517.95
Received: 03.02.2020
Revised: 29.05.2020
Accepted:09.06.2020

Citation: I. N. Dorofeeva, A. B. Rasulov, “Dirichlet problem for a generalized Cauchy–Riemann equation with a supersingular point on a half-plane”, Zh. Vychisl. Mat. Mat. Fiz., 60:10 (2020), 1734–1740; Comput. Math. Math. Phys., 60:10 (2020), 1679–1685

Citation in format AMSBIB
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\paper Dirichlet problem for a generalized Cauchy--Riemann equation with a supersingular point on a half-plane
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\vol 60
\issue 10
\pages 1734--1740
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