L-1-Uniqueness of the Fokker-Planck Equation on a Riemannian Manifold
L-1-Uniqueness of the Fokker-Planck Equation on a Riemannian Manifold
复制标题
黎曼流形上福克-普朗克方程的L-1-唯一性
DOI：
10.1007/s11118-018-9727-1
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发表时间：
2019
影响因子：
1.1
通讯作者：
Wu Liming
中科院分区：
文献类型：
--
作者：
Qian Bin;Wu Liming
本文给出了在开区间上Sturm-Liouville算子l∞唯一性的一个充分必要条件，等价于相关Fokker-Planck方程的l∞唯一性。通过与一维Sturm-Liouville算子的比较，我们得到了一类一般椭圆算子riemann流形的Fokker-Planck方程的1-唯一性的充分条件。进一步，作为的theL∞唯一性的直接结果，导出了1- liouville性质。
In this paper, we obtain a necessary and sufficient condition forL∞-uniqueness of Sturm-Liouville operatoron an open interval of, which is equivalent to theL1-uniqueness of the associated Fokker-Planck equation. For a general elliptic operatoron a Riemannian manifold, we obtain sharp sufficient conditions for theL1-uniqueness of the Fokker-Planck equation associated with, via comparison with a one-dimensional Sturm-Liouville operator. Furthermore theL1-Liouville property is derived as a direct consequence of theL∞-uniqueness of.