GRADIENT ESTIMATES FOR DIVERGENCE FORM ELLIPTIC SYSTEMS ARISING FROM COMPOSITE MATERIAL.

In this paper, we show that W^1,p (1 ≤ p < ∞ ) weak solutions to divergence form elliptic systems are Lipschitz and piecewise C¹ provided that the leading coefficients and data are of piecewise Dini mean oscillation, the lower-order coefficients are bounded, and interfacial boundaries are C^1,Dini. This extends a result of Li and Nirenberg [Comm. Pure Appl. Math., 56 (2003), pp. 892-925]. Moreover, under a stronger assumption on the piecewise L¹-mean oscillation of the leading coefficients, we derive a global weak-type (1,1) estimate with respect to A₁ Muckenhoupt weights for the elliptic systems without lower-order terms. [ABSTRACT FROM AUTHOR]