Abstract:
The paper studies how the statement of boundary value problems for a generalized Cauchy–Riemann equation is affected by nonisolated singularities in a lower-order coefficient of the equation assuming that these singularities are pairwise disjoint and do not pass through the origin. It turns out that posing only a condition on the boundary of the domain is insufficient in such problems. Therefore, we consider a case combining elements of the Riemann–Hilbert problem on the boundary of the domain and a linear transmission problem on the circles supporting the singularities in the lower-order coefficient inside the domain.
Keywords:generalized Cauchy–Riemann equation, singularity in a lower-order coefficient, Pompeiu–Vekua operator, Riemann–Hilbert problem, linear transmission problem.
Citation:
A. B. Rasulov, Yu. S. Fedorov, “On a statement of the boundary value problem for a generalized Cauchy–Riemann equation with nonisolated singularities in a lower-order coefficient”, Mat. Zametki, 116:1 (2024), 139–151; Math. Notes, 116:1 (2024), 119–129
\Bibitem{RasFed24}
\by A.~B.~Rasulov, Yu.~S.~Fedorov
\paper On a statement of the boundary value problem for a generalized Cauchy--Riemann equation with nonisolated singularities in a lower-order coefficient
\jour Mat. Zametki
\yr 2024
\vol 116
\issue 1
\pages 139--151
\mathnet{http://mi.mathnet.ru/mzm14219}
\crossref{https://doi.org/10.4213/mzm14219}
\transl
\jour Math. Notes
\yr 2024
\vol 116
\issue 1
\pages 119--129
\crossref{https://doi.org/10.1134/S0001434624070101}
Citation in format AMSBIB
Contact us: