Elliptic Equations with Degenerate Weights

We obtain new local Calderón--Zygmund estimates for elliptic equations with matrix-valued weights linear as well nonlinear equations. introduce a novel log-BMO condition on the weight $\mathbb M$. In particular, we assume smallness of logarithm in BMO. This allows us to include degenerate, discontinuous weights. The assumption parameter is sharp and terms integrability exponent gradient. novelty even setting nondegenerate compared previously known results, where dependency was exponential. provide examples that show sharpness norm.