  We obtain new local Calderon-Zygmund estimates for elliptic equations with
matrix-valued weights for linear as well as non-linear equations. We introduce
a novel log-BMO condition on the weight M. In particular, we assume smallness
of the logarithm of the matrix-valued weight in BMO. This allows to include
degenerate, discontinuous weights. We provide examples that show the sharpness
of the estimates in terms of the log-BMO-norm.
