Weighted W^{1,p} estimates for solutions of nonlinear parabolic equations

We are concerned with optimal regularity theory in weighted Sobolev spaces for discontinuous nonlinear parabolic problems in divergence form over a non-smooth bounded domain. Assuming smallness in BMO of the principal part of the nonlinear operator and flatness in Reifenberg sense of the boundary we establish a global weighted $W^{1,p}$ estimate for the weak solutions of such problems by proving that the spatial gradient and the nonhomogeneous term belong to the same weighted Lebesgue space. The result is new in the settings of nonlinear parabolic problems.