Partial regularity for local minimizers of functionals with double-phase Orlicz growth

In this paper, we consider the local minimizers to a class of non-autonomous functional with double-phase Orlicz growth: \begin{equation*} u \in W^{1,1}(Ω; \mathbb{R}^N) \mapsto \int_Ω\Big( {φ_1}\big(|Du|_{\mathbb{A}^u}\big) + a(x)\,{φ_2} \big(|Du|_{\mathbb{A}^u}\big) \Big)\, dx, \end{equation*} whe