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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2024 Volume 64, Number 11, Pages 2132–2142 (Mi zvmmf11868)

Partial Differential Equations

Integral representation of solutions and Riemann–Hilbert type problem for the Cauchy–Riemann equation with strong singularity in the lower order coefficient in a domain with piecewise smooth boundary

A. B. Rasulov, N. V. Yakivchik

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

Abstract: The goal of this work is to construct the general solution of the Cauchy–Riemann equation with strong singularities in the lower order coefficient and to study the Riemann–Hilbert boundary value problem in a domain with a piecewise smooth boundary.

Key words: Cauchy–Riemann equations, strong singularities in coefficient, Pompeiu–Vekua operator, piecewise smooth boundary, Riemann–Hilbert problem.

UDC: 517.95

Received: 21.04.2024
Revised: 21.04.2024
Accepted: 26.07.2024

DOI: 10.31857/S0044466924110086


 English version:
Computational Mathematics and Mathematical Physics, 2024, 64:11, 2643–2654

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© Steklov Math. Inst. of RAS, 2025