Gradient Estimates for Solutions to Divergence Form Elliptic Equations with Discontinuous Coefficients

Abstract

In this paper we derive global W 1,∞ and piecewise C 1,α estimates for solutions to divergence form elliptic equations with piecewise Hölder continuous coefficients. The novelty of these estimates is that, even though they depend on the shape and on the size of the surfaces of discontinuity of the coefficients, they are independent of the distance between these surfaces.