Second-order elliptic equations with variably partially VMO coefficients

N. V. Krylov

doi:10.1016/j.jfa.2009.06.014

Second-order elliptic equations with variably partially VMO coefficients

N. V. Krylov

School of Mathematics

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

54 Scopus citations

Abstract

The solvability in W_p² (R^d) spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal directions in each small ball with the direction depending on the ball. This generalizes to a very large extent the case of equations with continuous or VMO coefficients.

Original language	English (US)
Pages (from-to)	1695-1712
Number of pages	18
Journal	Journal of Functional Analysis
Volume	257
Issue number	6
DOIs	https://doi.org/10.1016/j.jfa.2009.06.014
State	Published - Sep 15 2009

Bibliographical note

Funding Information:
✩ The work was partially supported by NSF Grant DMS-0653121. E-mail address: [email protected].

Keywords

Partially VMO coefficients
Second-order elliptic equations
Sobolev spaces
Vanishing mean oscillation

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10.1016/j.jfa.2009.06.014

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title = "Second-order elliptic equations with variably partially VMO coefficients",

abstract = "The solvability in Wp2 (Rd) spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal directions in each small ball with the direction depending on the ball. This generalizes to a very large extent the case of equations with continuous or VMO coefficients.",

keywords = "Partially VMO coefficients, Second-order elliptic equations, Sobolev spaces, Vanishing mean oscillation",

author = "Krylov, {N. V.}",

note = "Funding Information: ✩ The work was partially supported by NSF Grant DMS-0653121. E-mail address: [email protected].",

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AU - Krylov, N. V.

N1 - Funding Information: ✩ The work was partially supported by NSF Grant DMS-0653121. E-mail address: [email protected].

PY - 2009/9/15

Y1 - 2009/9/15

N2 - The solvability in Wp2 (Rd) spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal directions in each small ball with the direction depending on the ball. This generalizes to a very large extent the case of equations with continuous or VMO coefficients.

AB - The solvability in Wp2 (Rd) spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal directions in each small ball with the direction depending on the ball. This generalizes to a very large extent the case of equations with continuous or VMO coefficients.

KW - Partially VMO coefficients

KW - Second-order elliptic equations

KW - Sobolev spaces

KW - Vanishing mean oscillation

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EP - 1712

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 6

ER -

Second-order elliptic equations with variably partially VMO coefficients

Abstract

Bibliographical note

Keywords

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