Weighted W^1,p estimates for solutions of non-linear parabolic equations over non-smooth domains

We are concerned with optimal regularity theory in weighted Sobolev spaces for discontinuous non-linear parabolic problems in divergence form over a non-smooth, bounded domain. Assuming smallness in BMO of the principal part of the non-linear operator and flatness in Reifenberg sense of the boundary, we establish a global weighted W1,p estimate for the weak solutions of such problems by proving that the spatial gradient and the non-homogeneous term belong to the same weighted Lebesgue space. The result is new in the settings of non-linear parabolic problems.