INTEGRAL IDENTITY AND MEASURE ESTIMATES FOR STATIONARY FOKKER-PLANCK EQUATIONS

• 成果类型: Article
• 署名作者: Huang, Wen; Ji, Min; Liu, Zhenxin; Yi, Yingfei
• 署名单位: Chinese Academy of Sciences; University of Science & Technology of China, CAS; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; Jilin University; University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP917
• 发表日期: 2015
• 页码: 1712-1730
• 关键词: invariant-measures; parabolic equations; REGULARITY; uniqueness; EXISTENCE

摘要

We consider a Fokker-Planck equation in a general domain in R-n with L-loc(p) drift term and W-loc(1,p) 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.