The plateau problem for the prescribed mean curvature equation

Abstract

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 and lt; I}, .i.e we look for a vector function X : B→R3 which satisfies the following system of nonlinear differential equations