Uniqueness of solutions to weak parabolic equations for measures

We study uniqueness of solutions of parabolic equations for measures mu(dt dx) = mu(t)(dx)dt of the type L*mu = 0, satisfying mu(t) -> nu as t -> 0, where each mu(t) is a probability measure on R-d L = partial derivative(t) + a(ij) (t,x)partial derivative(xi) partial derivative(xj) + b(i)(t,x)partial derivative(xj) is a differential operator on (0, T) x R-d and nu is a given initial measure. One main result is that uniqueness holds under uniform ellipticity and Lipschitz conditions on a(ij) but for b(i) merely local integrability and coercivity conditions are sufficient.