Filippo Chiarenza, Michele Frasca, Placido Longo, W2,p-Solvability of the Dirichlet Problem for Nondivergence Elliptic Equations with VMO Coefficients, Transactions of the American Mathematical Society, Vol. 336, No. 2 (Apr., 1993), pp. 841-853
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Chiarenza et al. (1993) studied this question.