### 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 |
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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 |

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### Keywords

- Martingale problem
- Second order equations
- Vanishing mean oscillation

### ASJC Scopus subject areas

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