If I know that `\Phi_\varepsilon` is bounded in L^`{\infty}`(`\mathbb{R}^{2d}`) and that `\nabla \Phi_\varepsilon` is bounded in L^`{\infty}`(`\mathbb{R}^{2d}`), is it true that `\nabla \Phi_\varepsilon \to \nabla \Phi`, where `\Phi` is the limit of `\Phi_\varepsilon` (in the weak sense)?