On linear and nonlinear Riemann-Hilbert problems for regular functions with values in a Clifford algebra (Q755931)

The author discusses the boundary value problems for regular functions with values in a Clifford algebra \[ {\bar \partial}w=0,\quad x\in {\mathbb{R}}\setminus \Gamma,\quad w^+(x)=G(x)w^-(x)+\lambda f(x,w^+(x),w^-(x)),\quad x\in \Gamma,\quad w^-(\infty)=0. \] Under some hypotheses, it is proved that the linear boundary value problem (where \(\lambda f(x,w^+(x),w^-(x))\equiv g(x))\) has a unique solution and the nonlinear boundary value problem has at least one solution.