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

This article is cited in 60 scientific papers (total in 60 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.


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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
\by V.~I.~Bogachev, N.~V.~Krylov, M.~R\"ockner
\paper Elliptic and parabolic equations for measures
\jour Uspekhi Mat. Nauk
\yr 2009
\vol 64
\issue 6(390)
\pages 5--116
\jour Russian Math. Surveys
\yr 2009
\vol 64
\issue 6
\pages 973--1078

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    1. Manita O.A., Shaposhnikov S.V., “Nonlinear parabolic equations for measures”, Dokl. Math., 86:3 (2012), 857–860  crossref  mathscinet  zmath  isi  elib  scopus
    2. 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
    3. 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
    4. 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
    5. 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
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