Calderón–Zygmund estimates and non-uniformly elliptic operators

We consider a class of non-uniformly nonlinear elliptic equations whose model is given by−div(|Du|p−2Du+a(x)|Du|q−2Du)=−div(|F|p−2F+a(x)|F|q−2F)−div(|Du|p−2Du+a(x)|Du|q−2Du)=−div(|F|p−2F+a(x)|F|q−2F) where p