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Elliptic Differential Equations with Coefficients Measurable with Respect to One Variable and VMO with Respect to the Others
Doyoon Kim, N. V. Krylov
Source 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.
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