  We extend and improve the results in \cite{DK16}: showing that weak solutions
to full elliptic equations in divergence form with zero Dirichlet boundary
conditions are continuously differentiable up to the boundary when the leading
coefficients have Dini mean oscillation and the lower order coefficients verify
certain conditions. Similar results are obtained for non-divergence form
equations. 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-negative
adjoint solutions to non-divergence form elliptic equations, when the leading
coefficients have Dini mean oscillation.
