Hölder continuity of the gradient of solutions of uniformly parabolic equations with conormal boundary conditions

Summary We study solutions of the conormal derivative problem for uniformly parabolic equations in divergence form. Under weak regularity hypotheses on the operator, the global Hölder continuity of the gradient of a weak solution is established. The method of proof is based on 5] and the results extend those in 7, Section V.7].Sponsored by the National Science Foundation under Grant DMS-8315545.