The Bounded Slope Condition for Functionals Depending on $x$, $u$, and $\nablau$

A global regularity result is proved for a class of minimizers of functionals of the form $\mathcal I(u)=\int_\Omega f(|\nabla u(x)|)+g(x,u(x))\,dx, u\in\phi+W^{1,1}_0(\Omega)$, where $\phi$ satisfies the Bounded Slope Condition.