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Russian Mathematical Surveys, 2009, Volume 64, Issue 6, Pages 973–1078
DOI: https://doi.org/10.1070/RM2009v064n06ABEH004652 (Mi rm9326) 		 
This article is cited in 89 scientific papers (total in 90 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
English version PDF (1242 kB) Citations (90)
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DOI: https://doi.org/10.1070/RM2009v064n06ABEH004652
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.
Received: 05.10.2009
Russian version:
Uspekhi Matematicheskikh Nauk, 2009, Volume 64, Issue 6(390), Pages 5–116
DOI: https://doi.org/10.4213/rm9326
Bibliographic databases:
Document Type: Article
UDC: 517.987+517.972
MSC: 35R05, 35R15, 35J15, 35K10, 58J65, 60J60
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 90 articles:
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