Summary: We consider solutions \(u \in W^{1, p}(\Omega; \mathbb{R}^N)\) of the \(p\)-Laplacian PDE \[\nabla \cdot(a(x) | D u |^{p - 2} D u) = 0,\]for \(x \in \Omega \subseteq \mathbb{R}^n\), where \(\Omega\) is open and bounded. More generally, we consider solutions of the elliptic system \[\nabla \cdot (a(x) g^\prime(a(x) | D u |) \frac{D u}{| D u |}) = 0, x \in \Omega\]as well as minimizers of the functional \[\int_\Omega g(a(x) | D u |) d x .\]In each case, the coefficient map \(a : \Omega \rightarrow \mathbb{R}\) is only assumed to be of class \(V M O(\Omega) \cap L^\infty(\Omega)\), which means that it may be discontinuous. Without assuming that \(x \mapsto a(x)\) has any weak differentiability, we show that \(u \in \mathcal{C}_{\text{loc}}^{0, \alpha}(\Omega)\) for each \(0 < \alpha < 1\). The preceding results are, in fact, a corollary of a much more general result, which applies to the functional \[\int_\Omega f(x, u, D u) d x\] in case \(f\) is only asymptotically convex.