Lq estimates of gradients for evolutional p-Laplacian systems

We study Lq-estimates of gradients for evolutional p-Laplacian systems with discontinuous coefficients and external force given by the divergence of BMO-functions. The result obtained here may be regarded as a partial generalization of the Calderon-Zygmund theory in Lq-estimate for the parabolic operator of second order to the evolutional p-Laplace operator.