Abstract
We study parabolic equations in divergence form with coefficients which are singular or degenerate as Muckenhoupt weight functions in one spatial variable. We establish weighted reverse Holder’s inequalities, and Lipschitz estimates for weak solutions of homogeneous equations with coefficients depending only on one spatial variable. We then use these results to prove interior, boundary, and global weighted estimates of Calderon-Zygmund type for weak solutions, assuming that the coefficients are partially vanishing mean oscillations with respect to the considered weights. The solvability in weighted Sobolev spaces is also achieved. Such results are new even for elliptic equations and our results can be readily extended to systems.
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