Elliptic equations for measures: Regularity and global bounds of densities

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

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We consider elliptic equations of the form L* μ = ν for measures on Rn. The membership of solutions in the Sobolev classes Wp, 1 (Rn) is established under appropriate conditions on the coefficients of L. Bounds of the form ρ{variant} (x) ≤ C Φ (x)-1 for the corresponding densities are obtained.

Original languageEnglish (US)
Pages (from-to)743-757
Number of pages15
JournalJournal des Mathematiques Pures et Appliquees
Issue number6
StatePublished - Jun 2006

Bibliographical note

Funding Information:
This work has been supported by the projects RFBR 04-01-00748, the Scientific Schools Grant 1758.2003.1, DFG 436 RUS 113/343/0(R), INTAS 03-51-5018, NSF Grant DMS-0140405, and the SFB 701 at the University of Bielefeld.


  • Elliptic equations for measures
  • Elliptic operators
  • Elliptic regularity
  • Invariant measures of diffusions
  • Sobolev spaces

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