Elliptic differential equations with measurable coefficients
Doyoon Kim, Nicolai V. Krylov · arXiv (Cornell University) · 2005
We prove the unique solvability of second order elliptic equations in non-divergence 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.