Bloch estimates in non-doubling generalized Orlicz spaces

We study minimizers of non-autonomous functionalsinf u circumflex accent cc(x, |Vu|) dx Omega when cc has generalized Orlicz growth. We consider the case where the upper growth rate of cc is unbounded and prove the Harnack inequality for minimizers. Our technique is based on "truncating" the function cc to approximate the minimizer and Harnack estimates with uniform constants via a Bloch estimate for the approximating minimizers.