Gradient estimates for divergence form parabolic systems from composite materials (Q829421)

The main results, that are gradient estimates and piecewise \(C^{\frac{1}{2}, 1}\)-regularity, are proved under the assumptions that the leading coefficients and data are of piecewise Dini mean oscillation. Moreover, the authors devote the study to a global weak type-\((1, 1)\) estimate with respect to \(A_1\) Muckenhoupt weights for solutions to suitable parabolic systems. In the ``Appendix'', the authors prove a weighted \(H^1_{p,\omega}\)-solvability and estimate for divergence form parabolic systems in nonsmooth domains with coefficients belonging to the Sarason class of vanishing mean oscillation (VMO) functions.