Integral identity and measure estimates for stationary Fokker.Planck equations

We consider a Fokker.Planck equation in a general domain in Rn with Lploc drift term and W1,ploc diffusion term for any p>n. By deriving an integral identity, we give several measure estimates of regular stationary measures in an exterior domain with respect to diffusion and Lyapunov-like or anti-Lyapunov-like functions. These estimates will be useful to problems such as the existence and nonexistence of stationary measures in a general domain as well as the concentration and limit behaviors of stationary measures as diffusion vanishes.