Abstract:
An integral representation is constructed and sufficient conditions are obtained for the existence of continuous solutions of the Carleman–Vekua equation with a singular point. The Riemann–Hilbert problem is analyzed for such an equation in the class of continuous functions.
\Bibitem{Tun93}
\by A.~Tungatarov
\paper On the theory of the~Carleman--Vekua equation with a~singular point
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 78
\issue 2
\pages 357--365
\mathnet{http://mi.mathnet.ru/eng/sm973}
\crossref{https://doi.org/10.1070/SM1994v078n02ABEH003473}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1220620}
\zmath{https://zbmath.org/?q=an:0833.30029}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994PD76700005}
Linking options:
https://www.mathnet.ru/eng/sm973
https://doi.org/10.1070/SM1994v078n02ABEH003473
https://www.mathnet.ru/eng/sm/v184/i3/p111
This publication is cited in the following 8 articles:
A. P. Soldatov, A. B. Rasulov, Springer Proceedings in Mathematics & Statistics, 357, Operator Theory and Harmonic Analysis, 2021, 535
N.K. Bliev, “On continuous solutions of the Carleman–Vekua equation with a singular point”, Complex Variables and Elliptic Equations, 2014, 1
A. Yu. Timofeev, “Kraevaya zadacha dlya obobschennogo uravneniya Koshi–Rimana v prostranstvakh, opisyvaemykh modulem nepreryvnosti”, Ufimsk. matem. zhurn., 4:1 (2012), 146–152
A. Y. Timofeev, “Construction of functions with determined behavior TG(b)(z) at a singular point”, Ufa Math. J., 3:1 (2011), 83–91
Heinrich Begehr, Dao-Qing Dai, “On continuous solutions of a generalized Cauchy–Riemann system with more than one singularity”, Journal of Differential Equations, 196:1 (2004), 67
Michael Reissig, Alexej Timofeev, “Special vekua equations with singular coefficients”, Applicable Analysis, 73:1-2 (1999), 187
D. Q. Dai, International Society for Analysis, Applications and Computation, 6, Complex Methods for Partial Differential Equations, 1999, 21
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