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We study the stationary Stokes system in divergence form. The coefficientsare assumed to be merely measurable in one direction and have Dini meanoscillations in the other directions. We prove that if $(u,p)$ is a weaksolution of the system, then $(Du,p)$ is bounded and its certain linearcombinations are continuous. We also prove a weak type-$(1,1)$ estimate for$(Du,p)$ under a stronger assumption on the $L^1$-mean oscillation of thecoefficients. The corresponding results up to the boundary on a half ball arealso established. These results are new even for elliptic equations andsystems.

Gradient estimates for Stokes systems with Dini mean oscillation coefficients