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J. Sib. Fed. Univ. Math. Phys., 2016, Volume 9, Issue 4, Pages 427–431 (Mi jsfu501)  

On an analogue of the Riemann–Hilbert problem for a non-linear perturbation of the Cauchy–Riemann operator

Yulia L. Cherepanova, Alexander A. Shlapunov

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: We consider a non-linear perturbation of a famous Riemann–Hilbert problem on the recovering of a holomorphic function in a domain via its real part on the boundary. We get an information on the local structure of the solutions and give sufficient conditions for their real analyticity. A simple instructive example is considered.

Keywords: the Cauchy-Riemann operator, non-linear Riemann-Hilbert problem.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00544_a
Ministry of Education and Science of the Russian Federation NSh-9149.2016.1
The work was supported by RFBR grant 14-01-00544 and the grant of President of Russian Federation for leading scientific schools NSh-9149.2016.1.


DOI: https://doi.org/10.17516/1997-1397-2016-9-4-427-431

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UDC: 517.95
Received: 16.08.2016
Received in revised form: 06.09.2016
Accepted: 15.10.2016
Language:

Citation: Yulia L. Cherepanova, Alexander A. Shlapunov, “On an analogue of the Riemann–Hilbert problem for a non-linear perturbation of the Cauchy–Riemann operator”, J. Sib. Fed. Univ. Math. Phys., 9:4 (2016), 427–431

Citation in format AMSBIB
\Bibitem{CheShl16}
\by Yulia~L.~Cherepanova, Alexander~A.~Shlapunov
\paper On an analogue of the Riemann--Hilbert problem for a non-linear perturbation of the Cauchy--Riemann operator
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2016
\vol 9
\issue 4
\pages 427--431
\mathnet{http://mi.mathnet.ru/jsfu501}
\crossref{https://doi.org/10.17516/1997-1397-2016-9-4-427-431}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000412010800003}


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  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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