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

Cite Download pdf To download PDF you should sign in

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: 14.10.2024). 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

Размещенный ниже текст является ознакомительной версией и может не соответствовать печатной

Readers community rating: votes 0

1. Bogachev V.I., Krylov N.V., Röckner M.// Comm. Partial Differ. Equ. 2001. V. 26. P. 2037—2080.

2. Bogachev V.I., Krylov N.V., Rekner M.// Uspekhi mat. nauk. 2009. T. 64, N 6. S. 5116.

3. Bogachev V.I., Krylov N.V., Röockner M., Shaposhnikov S.V. Fokker—Planck—Kolmogorov equations. Amer. Math. Soc., Rhode Island, Providence, 2015.

4. Bogachev V.I., Röckner M.// J. Funct. Anal. 1995. V. 133. P. 168—223.

5. Metafune G., Pallara D., Rhandi A.// J. Funct. Anal. 2005. V. 223. P. 396—424.

6. Bogachev V.I., Krylov N.V., Röckner M.// J. Math. Pures Appl. 2006. V. 85. P. 743—757.

7. Bourgain J., Brezis H.// J. Eur. Math. Soc. 2007. V. 9. P. 277—315.

8. Conti S., Faraco D., Maggi F.// Arch. Rational Mech. Anal. 2005. V. 175. P. 287—300.

9. Dacorogna B., Fusco N., Tartar L.// Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 2003. V. 14. P. 239—245.

10. Lunardi A., Metafune G.// Differ. Integral Equ. 2004. V. 17, N 1-2. P. 73—97.

11. Maz'ya V.// J. Eur. Math. Soc. 2010. V. 12. P. 221—240.

12. Ornstein D.// Arch. Rational Mech. Anal. 1962. V. 11. P. 40—49.

13. Chung L.O.// Proc. Amer. Math. Soc. 1983. V. 88. P. 531—532.

14. Li P., Schoen R.// Acta Math. 1984. V. 153, N 3-4. P. 279—301.

15. Bogachev V.I., Shaposhnikov S.V.// Annali Matem. Pura Appl. 2017. V. 196, N 5. P. 1609—1635.