  A popular and efficient discretization of evolutions involving the singular
$p$-Laplace operator is based on a factorization of the differential operator
into a linear part which is treated implicitly and a regularized singular
factor which is treated explicitly. It is shown that an unconditional energy
stability property for this semi-implicit time stepping strategy holds. Related
error estimates depend critically on a required regularization parameter.
Numerical experiments reveal reduced experimental convergence rates for smaller
regularization parameters and thereby confirm that this dependence cannot be
avoided in general.
