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Nicolai Krylov, University of Minnesota
On parabolic and elliptic equations with 
-coefficients
Abstract: 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.
We also investigate the unique solvability of second order parabolic equations in non-divergence form in 
, 
. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables.
From these results, we obtain the weak uniqueness of the martingale problem associated with PDEs.