Uniqueness of solutions to weak parabolic equations for measures
Vladimir Igorevich Bogachev, Giuseppe Da Prato, Michael Röckner, Wilhelm Stannat · Bulletin of the London Mathematical Society · 2007
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 R d , L = ∂ t + a i j ( t , x ) ∂ x i ∂ x j + b i ( t , x ) ∂ x j 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.