Elliptic equations for measures: Regularity and global bounds of densities

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

doi:10.1016/j.matpur.2005.11.006

Elliptic equations for measures: Regularity and global bounds of densities

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

School of Mathematics

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

We consider elliptic equations of the form L^* μ = ν for measures on Rⁿ. The membership of solutions in the Sobolev classes W^{p, 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 language	English (US)
Pages (from-to)	743-757
Number of pages	15
Journal	Journal des Mathematiques Pures et Appliquees
Volume	85
Issue number	6
DOIs	https://doi.org/10.1016/j.matpur.2005.11.006
State	Published - 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.

Keywords

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

Publisher link

10.1016/j.matpur.2005.11.006

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title = "Elliptic equations for measures: Regularity and global bounds of densities",

abstract = "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.",

keywords = "Elliptic equations for measures, Elliptic operators, Elliptic regularity, Invariant measures of diffusions, Sobolev spaces",

author = "Bogachev, {Vladimir I.} and Krylov, {Nicolai V.} and Michael R{\"o}ckner",

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.",

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doi = "10.1016/j.matpur.2005.11.006",

language = "English (US)",

volume = "85",

pages = "743--757",

journal = "Journal des Mathematiques Pures et Appliquees",

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publisher = "Elsevier Masson s.r.l.",

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TY - JOUR

T1 - Elliptic equations for measures

T2 - Regularity and global bounds of densities

AU - Bogachev, Vladimir I.

AU - Krylov, Nicolai V.

AU - Röckner, Michael

N1 - 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.

PY - 2006/6

Y1 - 2006/6

N2 - 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.

AB - 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.

KW - Elliptic equations for measures

KW - Elliptic operators

KW - Elliptic regularity

KW - Invariant measures of diffusions

KW - Sobolev spaces

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DO - 10.1016/j.matpur.2005.11.006

M3 - Article

AN - SCOPUS:33744917013

SN - 0021-7824

VL - 85

SP - 743

EP - 757

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 6

ER -

Elliptic equations for measures: Regularity and global bounds of densities

Abstract

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