On a nonlinear electrolysis problem

A mathematical model proposed by H. Amann for electrochemical reactions is considered. The model is considered in the steady-state case for two differently charged components of a solution. In this case the model reduces to a quasilinear system of two elliptic equations with nonlinear Neumann boundary conditions. In the regular case it is proved that this nonlinear problem is globally solvable in a Sobolev space $W_p^2(\Omega)$ with $p>n$ ($\Omega\subset\mathbb{R}^n$).