On the Local boundedness and higher integrability for the subcritical doubly nonlinear parabolic systems

We consider the inhomogeneous doubly nonlinear parabolic systems of the form \begin{equation*}\partial_t (|u|^{q-1}u)-\operatorname{div}(|Du|^{p-2}Du)=\operatorname{div}(|F|^{p-2}F)\end{equation*} in a bounded space-time cylinder $Ω_T=Ω\times(0,T)\subset \mathbb{R}^{N+1}$. We study the local regular