Continuity of weak solutions of elliptic partial differential equations

The continuity of weak solutions of elliptic partial differential equations is considered under minimal structure assumptions. The main result guarantees the continuity at the pointx ₀ for weakly monotone weak solutions if the structure ofA is controlled in a sequence of annuli with uniformly bounded ratioR _j /r _j such that lim _j→∞ R _j =0. As a consequence, we obtain a sufficient condition for the continuity of mappings of finite distortion.