Gradient estimates for parabolic \(\mathcal A\)-harmonic equations (Q622390)

The author obtains gradient estimates in Sobolev spaces and Orlicz spaces for weak solutions of the following parabolic \({\mathcal A}\)-harmonic equation \[ u_t-\text{div}\, {\mathcal A}(\nabla u,x,t)= \text{div}\, (|{\mathbf f}|^{p-2}{\mathbf f}) \quad \text{in }\Omega_T=\Omega\times(0,T], \] where \({\mathbf f}\) and \({\mathcal A}\) are given vector fields satisfying suitable conditions.