Gradient type estimates for linear elliptic systems from composite materials

In this paper, we consider linear elliptic systems from composite materials where the coefficients depend on the shape and might have the discontinuity between the subregions. We derive a function which is related to the gradient of the weak solutions and which is not only locally piecewise H¨older continuous but locally H¨older continuous. The gradient of the weak solutions can be estimated by this derived function and we also prove the local piecewise gradient H¨older continuity which was obtained by the previous results.