We prove that the problem Minimize integral(Omega) g(Phi(del T(x)))dx, T is an element of T-B + W-0(1,infinity)(Omega, R(n)) admits at least one solution for any lower-semicontinuous extended valued function g, for any quasi-affine real-valued function Phi, and for any piecewise-affine boundary datum T-B such that Phi(del T-B) is constant.