Integral identity and measure estimates for stationary Fokker-Planck equations. (English) Zbl 1319.35268

Summary: We consider a Fokker-Planck equation in a general domain in \(\mathbb{R}^{n}\) with \(L^{p}_{\mathrm{loc}}\) drift term and \(W^{1,p}_{\mathrm{loc}}\) 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.


35Q84 Fokker-Planck equations
60J60 Diffusion processes
37B25 Stability of topological dynamical systems
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