Singular parabolic p-Laplacian systems under non-smooth external forces. Regularity up to the boundary

We study the regularity of the solutions to initial-boundary value problems for N-systems of the p-Laplacian type, in $n\ge 3$ space variables, with square-integrable external forces in the space-time cylinder. So, the ellipticity coefficient remains unbounded. The singular case $\mu =0$ is covered.