  In this paper we discuss the optimal regularity of the variable coefficient
parabolic Signorini problem with $W^{1,1}_p$ coefficients and $L^p$
inhomogeneity, where $p>n+2$ with $n$ being the space dimension. Relying on an
parabolic Carleman estimate and an epiperimetric inequality, we show the
optimal regularity of the solutions as well as the regularity of the regular
free boundary.
