PIECEWISE CONTINUOUS SOLUTIONS OF NONLINEAR ELLIPTIC-EQUATIONS IN THE PLANE

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 natual growth condition with sigma > 0. \f(z,W)\ less-than-or-equal-to F(z)\W\sigma.