  We consider elliptic equations and systems in divergence form with the
conormal or the Robin boundary conditions, with small BMO (bounded mean
oscillation) or variably partially small BMO coefficients. We propose a new
class of domains which are locally close to a half space (or convex domains)
with respect to the Lebesgue measure in the system (or scalar, respectively)
case, and obtain the $W^1_p$ estimate for the conormal problem with the
homogeneous boundary condition. Such condition is weaker than the Reifenberg
flatness condition, for which the closeness is measured in terms of the
Hausdorff distance, and the semi-convexity condition. For the conormal problem
with inhomogeneous boundary conditions, we also assume that the domain is
Lipschitz. By using these results, we obtain the $W^1_p$ and weighted $W^1_p$
estimates for the Robin problem in these domains.

Analysis of PDEs