  We study a class of second-order elliptic equations of divergence form, with
discontinuous coefficients and data, which models the conductivity problem in
composite materials. We establish optimal gradient estimates by showing the
explicit dependence of the elliptic coefficients and the distance between
interfacial boundaries of inclusions. The novelty of these estimates is that
they unify the known results in the literature and answer open problem (b)
proposed by Li-Vogelius (2000) for the isotropic conductivity problem. We also
obtain more interesting higher-order derivative estimates, which answers open
problem (c) of Li-Vogelius (2000). It is worth pointing out that the equations
under consideration in this paper are nonhomogeneous.
