Abstract
We establish global weighted W2,p, 2 < p < ∞, estimates for the solution to the Dirichlet problem for an elliptic equation in nondivergence form with BMO coefficients in a C1,1 domain under the assumption that the matrix of the coefficients has a small BMO semi-norm while the associated weight belongs to a Muckenhoupt class. These conditions are weaker than those reported in the literature.
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