A second order,non-linear elliptic boundary value problem with generalized Goursat data

Summary In this paper the case of generalized Goursat data is considered for the non-linear partial differential equation Δu = f(x, y, u, u_x, u_y). The existence and uniqueness of a solution is demonstrated, under certain conditions, by employing the contraction mapping method in a suitable Banach space. This research was supported in part at the Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, by the National Science Foundation under Grants GP-2067, GP-3937, and in part by the Air Force Office of Scientific Research under Grant AFOSR 400-64, and at Georgetown University, Washington, D.C., by the National Science Foundation under Grant GP-1650 and GP-5023.