Hölder continuity of weak solutions of p-Laplacian PDEs with VMO coefficients

We consider solutions of the -Laplacian PDE for , where is open and bounded. More generally, we consider solutions of the elliptic system as well as minimizers of the functional In each case, the coefficient map is only assumed to be of class , which means that it may be discontinuous. Without assuming that has any weak differentiability, we show that for each . The preceding results are, in fact, a corollary of a much more general result, which applies to the functional in case is only asymptotically convex.