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We obtain new partial H\"older continuity results for solutions to divergenceform elliptic systems with discontinuous coefficients, obeying $p(x)$-typenonstandard growth conditions. By an application of the method of$\mathcal{A}$-harmonic approximation, we are able to allow for bothVMO-discontinuities in the coefficients, and the minimal $\log$-H\"olderregularity assumption on the exponent function. In doing so, we recover a localversion of the quantisation phenomenon characteristic continuous coefficientcase.

Partial continuity for nonlinear systems with nonstandard growth and discontinuous coefficients