Elliptic Equations in Divergence Form with Discontinuous Coefficients in Domains with Corners

Abstract: We study the equations in divergence form with piecewise $C^{\ga}$ coefficients. The domains contain corners and the discontinuity surfaces are attached to edges of the corners. We obtain piecewise $C^{1,\ga}$ estimates across the discontinuity surfaces and provide an example to illustrate the issue about the regularity at the corners.