Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others

Doyoon Kim; N. V. Krylov

doi:10.1137/050646913

Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others

Doyoon Kim, N. V. Krylov

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

89 Citations (Scopus)

Abstract

We prove the unique solvability of second order elliptic equations in nondivergence form in Sobolev spaces. The coefficients of the second order terms are measurable in one variable and VMO in other variables. From this result, we obtain the weak uniqueness of the Martingale problem associated with the elliptic equations.

Original language	English
Pages (from-to)	489-506
Number of pages	18
Journal	SIAM Journal on Mathematical Analysis
Volume	39
Issue number	2
DOIs	https://doi.org/10.1137/050646913
Publication status	Published - 2007
Externally published	Yes

Keywords

Martingale problem
Second order equations
Vanishing mean oscillation

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/050646913

Cite this

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title = "Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others",

abstract = "We prove the unique solvability of second order elliptic equations in nondivergence form in Sobolev spaces. The coefficients of the second order terms are measurable in one variable and VMO in other variables. From this result, we obtain the weak uniqueness of the Martingale problem associated with the elliptic equations.",

keywords = "Martingale problem, Second order equations, Vanishing mean oscillation",

author = "Doyoon Kim and Krylov, {N. V.}",

year = "2007",

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T1 - Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others

AU - Kim, Doyoon

AU - Krylov, N. V.

PY - 2007

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N2 - We prove the unique solvability of second order elliptic equations in nondivergence form in Sobolev spaces. The coefficients of the second order terms are measurable in one variable and VMO in other variables. From this result, we obtain the weak uniqueness of the Martingale problem associated with the elliptic equations.

AB - We prove the unique solvability of second order elliptic equations in nondivergence form in Sobolev spaces. The coefficients of the second order terms are measurable in one variable and VMO in other variables. From this result, we obtain the weak uniqueness of the Martingale problem associated with the elliptic equations.

KW - Martingale problem

KW - Second order equations

KW - Vanishing mean oscillation

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U2 - 10.1137/050646913

DO - 10.1137/050646913

M3 - Article

AN - SCOPUS:41449093759

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VL - 39

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EP - 506

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 2

ER -

Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others

Abstract

Keywords

ASJC Scopus subject areas

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