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

Occupation: Professor
Affiliation:
Lomonosov Moscow State University
National Research University “Higher School of Economics”
St. Tikhons Orthodox University
Address: Russian Federation, Moscow

S. Popova

Occupation:
Affiliation: Lomonosov Moscow State University
Address: Russian Federation, Moscow

Stanislav Shaposhnikov

Occupation:
Affiliation:
Lomonosov Moscow State University
National Research University “Higher School of Economics”
St. Tikhons Orthodox University
Address: Russian Federation, Moscow

Journal name

Doklady Akademii nauk

Edition

Volume 482 Issue 6

Pages

631-634

Abstract

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^1,1(R^d). There is also a version of this result for densities with respect to Gaussian measures.

Keywords

Received

10.12.2018

Publication date

13.12.2018

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GOST	Bogachev V., Popova S., Shaposhnikov S. On Sobolev Classes Containing Solutions to Fokker–Planck–Kolmogorov Equations // Doklady Akademii nauk – 2018. – V. 482. – Issue 6 C. 631-634 [Electronic resource]. URL: http://ras.jes.su/dan/s086956520002913-7-1-en (circulation date: 29.04.2024). DOI: 10.31857/S086956520002913-7
MLA	Bogachev, Vladimir, Popova, S., Shaposhnikov, Stanislav "On Sobolev Classes Containing Solutions to Fokker–Planck–Kolmogorov Equations." Doklady Akademii nauk 482.6 (2018):631-634. DOI: 10.31857/S086956520002913-7
APA	Bogachev V., Popova S., Shaposhnikov S. (2018). On Sobolev Classes Containing Solutions to Fokker–Planck–Kolmogorov Equations. Doklady Akademii nauk 482(6), pp.631-634 DOI: 10.31857/S086956520002913-7

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