The plateau problem for the prescribed mean curvature equation

Given a Jordan curve r in Tin R³ and H : R³ → R³  a continuous and bounded function, we consider the Plateau problem in the unit disc B = {(u, v) ∈ R³ ; u² +v² < I}, .i.e we look for a vector function X : B→R³ which satisfies the following system of nonlinear differential equations