Bloch estimates in non-doubling generalized Orlicz spaces

<abstract><p>We study minimizers of non-autonomous functionals</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} \inf\limits_u \int_\Omega \varphi(x,|\nabla u|) \, dx \end{align*} $\end{document} </tex-math></disp-formula></p> <p>when $ \varphi has generalized Orlicz growth. We consider the case where upper growth rate is unbounded and prove Harnack inequality for minimizers. Our technique based on "truncating" function to approximate minimizer estimates with uniform constants via a Bloch estimate approximating minimizers.</p></abstract>