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Uspekhi Mat. Nauk, 2009, Volume 64, Issue 6(390), Pages 5–116 (Mi umn9326)  

This article is cited in 71 scientific papers (total in 71 papers)

Elliptic and parabolic equations for measures

V. I. Bogacheva, N. V. Krylovb, M. Röcknerc

a M. V. Lomonosov Moscow State University
b University of Minnesota, Minneapolis, USA
c Bielefeld University, Germany

Abstract: This article gives a detailed account of recent investigations of weak elliptic and parabolic equations for measures with unbounded and possibly singular coefficients. The existence and differentiability of densities are studied, and lower and upper bounds for them are discussed. Semigroups associated with second-order elliptic operators acting in $L^p$-spaces with respect to infinitesimally invariant measures are investigated.
Bibliography: 181 titles.

Keywords: elliptic equation, parabolic equation, stationary distribution of a diffusion process, transition probability.

DOI: https://doi.org/10.4213/rm9326

Full text: PDF file (1460 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2009, 64:6, 973–1078

Bibliographic databases:

UDC: 517.987+517.972
MSC: 35R05, 35R15, 35J15, 35K10, 58J65, 60J60
Received: 05.10.2009

Citation: V. I. Bogachev, N. V. Krylov, M. Röckner, “Elliptic and parabolic equations for measures”, Uspekhi Mat. Nauk, 64:6(390) (2009), 5–116; Russian Math. Surveys, 64:6 (2009), 973–1078

Citation in format AMSBIB
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    4. Bogachev V.I., Korolev A.V., Pilipenko A.Yu., “Non uniform averagings in the ergodic theorem for stochastic flows”, Dokl. Math., 81:3 (2010), 422–425  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
    5. Shaposhnikov S.V., “Estimates of Solutions of Parabolic Equations for Measures”, Dokl. Math., 82:2 (2010), 769–772  crossref  mathscinet  zmath  isi  elib  elib  scopus
    6. Bogachev V.I., Kirillov A.I., Shaposhnikov S.V., “Invariant Measures of Diffusions with Gradient Drifts”, Dokl. Math., 82:2 (2010), 790–793  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. Bogachev V.I., Röckner M., Shaposhnikov S.V., “On uniqueness problems related to elliptic equations for measures”, J. Math. Sci., 176:6 (2011), 759–773  crossref  mathscinet  zmath  elib  scopus
    8. Bogachev V.I., Kirillov A.I., Shaposhnikov S.V., “On probability and integrable solutions to the stationary Kolmogorov equation”, Dokl. Math., 83:3 (2011), 309–313  crossref  mathscinet  zmath  isi  elib  elib  scopus
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