GENERALIZATION OF RIEMANN-HILBERT BOUNDARY
VALUE PROBLEM FOR A FIRST ORDER NONLINEAR
COMPLEX PARTIAL DIFFERENTIAL EQUATION
Abstract. In this paper we discuss on the existence and uniqueness solution of the Riemann-Hilbert boundary value problem in the form:
\begin{displaymath}
\frac{\partial w}{\partial \bar{z}}=F(z,w,\frac{\partial w}{\partial z})+G(z,w,\bar{w}), \quad\quad z\in{D},
\end{displaymath} (1)


\begin{displaymath}
Re(a+ib)w=g\quad\quad \mbox{on} \quad \partial D \quad\quad
\end{displaymath} (2)

in $C_{1,\alpha}(\bar{D})$, where $a$, $b$ and $g$ are given Holder continuously differentiable real-valued functions of a real parameter $t$ on $\partial{D}$. We shall assume that $ a^2+b^2=1$ everywhere on $\partial{D}$.
AMS Subject Classification: 35D05, 35J55, 35J67


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DOI: 10.12732/ijam.v29i1.1

Volume: 29
Issue: 1
Year: 2016