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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.
DOI:
https://doi.org/10.4213/rm9326
Full text:
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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
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Linking options:
http://mi.mathnet.ru/eng/umn9326https://doi.org/10.4213/rm9326 http://mi.mathnet.ru/eng/umn/v64/i6/p5
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