On the equivalence of two variational problems

We consider the following problems Minimize I(u) = integral (Omega)f(delu(x)) + g(x, u(x))dz on {u epsilon W-0(1,p)(Omega) : u(-)(x) less than or equal to u(x) less than or equal tou(+)(x)} Minimize I(u) = integral (Omega)f(delu(x)) + g(x, u(x))dz on {u epsilon W-0(1,infinity)(Omega) : delu(x) epsilon K} where f : R-n --> R is a convex function, Omega is an open bounded subset of R, K is a closed convex subset of R-n such that 0 epsilon int K and u(-) and u(+) are suitable obstacles. We give conditions on the function g under which the two problems are equivalent.