  We consider differential operators defined as Friedrichs extensions of
quadratic forms with non-smooth coefficients. We prove a two term optimal
asymptotic for the Riesz means of these operators and thereby also reprove an
optimal Weyl law under certain regularity conditions. The methods used are then
extended to consider more general admissible operators perturbed by a rough
differential operator and obtaining optimal spectral asymptotics again under
certain regularity conditions. For the Weyl law we assume the coefficients are
differentiable with H\"older continuous derivatives and for the Riesz means we
assume the coefficients are two times differentiable with H\"older continuous
derivatives.
