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JOURNALS // Uspekhi Matematicheskikh Nauk // Archive

Uspekhi Mat. Nauk, 2009 Volume 64, Issue 6(390), Pages 5–116 (Mi rm9326)

This article is cited in 95 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.

UDC: 517.987+517.972

MSC: 35R05, 35R15, 35J15, 35K10, 58J65, 60J60

Received: 05.10.2009

DOI: 10.4213/rm9326


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

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