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

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 su cient conditions for their real analyticity. A simple instructive example is considered.