### 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 | |

Publication status | Published - 2007 Dec 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Martingale problem
- Second order equations
- Vanishing mean oscillation

### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Applied Mathematics
- Numerical Analysis

### Cite this

**Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others.** / Kim, Doyoon; Krylov, N. V.

Research output: Contribution to journal › Article

*SIAM Journal on Mathematical Analysis*, vol. 39, no. 2, pp. 489-506. https://doi.org/10.1137/050646913

}

TY - JOUR

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 - 2007/12/1

Y1 - 2007/12/1

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

UR - http://www.scopus.com/inward/record.url?scp=41449093759&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41449093759&partnerID=8YFLogxK

U2 - 10.1137/050646913

DO - 10.1137/050646913

M3 - Article

VL - 39

SP - 489

EP - 506

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 2

ER -