Partial continuity for nonlinear systems with nonstandard growth and discontinuous coefficients

We obtain new partial Hölder continuity results for solutions to divergence form elliptic systems with discontinuous coefficients, obeying p(x)-type nonstandard growth conditions. By an application of the method of 𝒜-harmonic approximation, we are able to allow for both VMO-discontinuities in the coefficients, and the minimal log-Hölder regularity assumption on the exponent function. In doing so, we recover a local version of the quantisation phenomenon characteristic continuous coefficient case.