Elliptic and parabolic equations for measures

Vladimir I. Bogachev, Nikolai V. Krylov, Michael Röckner

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


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 Lp-spaces with respect to infinitesimally invariant measures are investigated.

Original languageEnglish (US)
Pages (from-to)973-1078
Number of pages106
JournalRussian Mathematical Surveys
Issue number6
StatePublished - 2009


  • Elliptic equation
  • Parabolic equation
  • Stationary distribution of a diffusion process
  • Transition probability


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