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arXiv · 1401.7707

Integral identity and measure estimates for stationary Fokker-Planck equations

Wen Huang·Min Ji·Zhenxin Liu·Yingfei Yi
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Abstract

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.

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Wen Huang, Min Ji, Zhenxin Liu, Yingfei Yi. 2015-09-09. Integral identity and measure estimates for stationary Fokker-Planck equations. https://doi.org/10.1214/14-aop917

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