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We extend and improve the results in \cite{DK16}: showing that weak solutionsto full elliptic equations in divergence form with zero Dirichlet boundaryconditions are continuously differentiable up to the boundary when the leadingcoefficients have Dini mean oscillation and the lower order coefficients verifycertain conditions. Similar results are obtained for non-divergence formequations. We extend the weak type-(1, 1) estimates in \cite{DK16} and\cite{Es94} up to the boundary and derive a Harnack inequality for non-negativeadjoint solutions to non-divergence form elliptic equations, when the leadingcoefficients have Dini mean oscillation.

On $C^1$, $C^2$, and weak type-$(1,1)$ estimates for linear elliptic operators: Part II