Representations of solutions to Fokker-Planck-Kolmogorov equations with coefficients of low regularity

被引：3
|
作者：
Bogachev, Vladimir, I [1 ]
Shaposhnikov, Stanislav, V [1 ,2 ]
机构：
[1] Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow, Russia
[2] Natl Res Univ Higher Sch Econ, Moscow, Russia
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2020年 / 20卷 / 02期
基金：
俄罗斯基础研究基金会;
关键词：
Fokker-Planck-Kolmogorov equation; Double divergence form equation; Representation of solutions; TRANSITION-PROBABILITIES; PARABOLIC EQUATIONS; CONTINUITY;
D O I：
10.1007/s00028-019-00532-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove a formula representing solutions to parabolic Fokker-Planck-Kolmogorov equations with coefficients of low regularity. This formula is applied for proving the continuity of solution densities under broad assumptions and obtaining upper bounds for them. In the case of diffusion coefficients of class VMOx we show that the solution density is locally integrable to any power.
引用
收藏
页码：355 / 374
页数：20
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