Partial continuity for a class of elliptic systems with non-standard growth

We study partial Holder continuity of weak solutions to elliptic systems with variable non-standard growth, which are related to the function $\Phi(x,t):=t^{p(x)}\log(e+t)$. We prove that weak solutions are Holder continuous for any Holder exponent, except Lebesgue measure zero sets, if systems satisfy certain continuity assumptions. In particular, the variable exponent functions p(.) are assumed to satisfy so-called vanishing log-Holder continuity