  We show that any weak solution to elliptic equations in divergence form is
continuously differentiable provided that the modulus of continuity of
coefficients in the $L^1$-mean sense satisfies the Dini condition. This in
particular answers a question recently raised by Yanyan Li and allows us to
improve a result of Brezis. We also prove a weak type-$(1,1)$ estimate under a
stronger assumption on the modulus of continuity. The corresponding results for
non-divergence form equations are also established.
