Abstract: The Riemann boundary value problem is solved for the nonlinear elliptic equation in the plane
W_z=H(z,W,W_z) + f(z,W).The function H is Lipschitz continuous with respect to the last two variables, with the Lipschitz constant for the last variable being strictly less than one (ellipticity condition). While the function f satisfies a natural growth condition with σ > 0.
|f(z,W)| ≤ F(z)|W|^σ.