Uniqueness of solutions to weak parabolic equations for measures

We study uniqueness of solutions of parabolic equations for measures μ(dt dx) = μt(dx)dt of the type L* μ = 0, satisfying μt → ν as t → 0, where each μt is a probability measure on ℝd, L = ∂t + aij(t, x)∂xi∂xj + bi(t, x)∂xj is a differential operator on (0, T) × ℝd and ν is a given initial measure. One main result is that uniqueness holds under uniform ellipticity and Lipschitz conditions on aij but for bi merely local integrability and coercivity conditions are sufficient.