On Sobolev Classes Containing Solutions to Fokker-Planck-Kolmogorov Equations

被引：0

作者：

Bogachev, V. I. ^{[1
,2
,3
]}

Popova, S. N. ^{[1
]}

Shaposhnikov, S. V. ^{[1
,2
,3
]}

机构：

[1] Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow 119991, Russia

[2] Natl Res Univ, Higher Sch Econ, Moscow, Russia

[3] St Tikhons Orthodox Univ, Moscow, Russia

来源：

DOKLADY MATHEMATICS | 2018年 / 98卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

DIFFERENTIAL-OPERATORS; ELLIPTIC-EQUATIONS; INVARIANT-MEASURES; REGULARITY; INEQUALITY;

D O I：

10.1134/S1064562418060273

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main result of this paper answers negatively a long-standing question and shows that a density of a probability measure satisfying the Fokker-Planck-Kolmogorov equation with a drift integrable with respect to this density can fail to belong to the Sobolev class W-1,W-1((d)). There is also a version of this result for densities with respect to Gaussian measures. On the other hand, we prove that the solution density belongs to certain fractional Sobolev classes.

引用

页码：498 / 501

页数：4

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