Interior Calderón–Zygmund estimates for solutions to general parabolic equations of p-Laplacian type

We study general parabolic equations of the form u t = div A ( x , t , u , D u ) + div ( | F | p - 2 F ) + f whose principal part depends on the solution itself. The vector field A is assumed to have small mean oscillation in x , measurable in t , Lipschitz continuous in u , and its growth in Du is like the p -Laplace operator. We establish interior Calderón–Zygmund estimates for locally bounded weak solutions to the equations when p > 2 n / ( n + 2 ) . This is achieved by employing a perturbation method together with developing a two-parameter technique and a new compactness argument. We also make crucial use of the intrinsic geometry method by DiBenedetto (Degenerate parabolic equations, Springer, New York, 1993 ) and the maximal function free approach by Acerbi and Mingione (Duke Math J 136(2):285–320, 2007 ).