Gradient estimates for parabolic systems from composite material.

In this paper, we derive W and piecewise C estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise Hölder continuous in space variables x and smooth in t. This is an extension to parabolic systems of results of Li and Nirenberg [Comm Pure Appl Math, 2003, 56: 892-925] on elliptic systems. These estimates depend on the shape and the size of the surfaces of discontinuity of the coefficients, but are independent of the distance between these surfaces. [ABSTRACT FROM AUTHOR]