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

 
PIIS086956520002913-7-1
DOI10.31857/S086956520002913-7
Publication type Article
Status Published
Authors
Occupation: Professor
Affiliation:
Lomonosov Moscow State University
National Research University “Higher School of Economics”
St. Tikhons Orthodox University
Address: Russian Federation, Moscow
Occupation: 
Affiliation: Lomonosov Moscow State University
Address: Russian Federation, Moscow
Occupation: 
Affiliation:
Lomonosov Moscow State University
National Research University “Higher School of Economics”
St. Tikhons Orthodox University
Address: Russian Federation, Moscow
Journal nameDoklady Akademii nauk
EditionVolume 482 Issue 6
Pages631-634
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
Received10.12.2018
Publication date13.12.2018
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