Geodesic
On an analogue of the Riemann--Hilbert problem for a non-linear perturbation of the Cauchy--Riemann operator
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 4, pp. 427-431

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{JSFU_2016_9_4_a2,
     author = {Yulia L. Cherepanova and Alexander A. Shlapunov},
     title = {On an analogue of the {Riemann--Hilbert} problem for a non-linear perturbation of the {Cauchy--Riemann} operator},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {427--431},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2016_9_4_a2/}
}
TY  - JOUR
AU  - Yulia L. Cherepanova
AU  - Alexander A. Shlapunov
TI  - On an analogue of the Riemann--Hilbert problem for a non-linear perturbation of the Cauchy--Riemann operator
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2016
SP  - 427
EP  - 431
VL  - 9
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2016_9_4_a2/
LA  - en
ID  - JSFU_2016_9_4_a2
ER  - 
%0 Journal Article
%A Yulia L. Cherepanova
%A Alexander A. Shlapunov
%T On an analogue of the Riemann--Hilbert problem for a non-linear perturbation of the Cauchy--Riemann operator
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2016
%P 427-431
%V 9
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2016_9_4_a2/
%G en
%F JSFU_2016_9_4_a2
Yulia L. Cherepanova; Alexander A. Shlapunov. On an analogue of the Riemann--Hilbert problem for a non-linear perturbation of the Cauchy--Riemann operator. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 4, pp. 427-431. http://geodesic.mathdoc.fr/item/JSFU_2016_9_4_a2/