On the regularity of weak solutions to H-systems

We prove that every weak solution to the H-surface equation is locally bounded, provided the prescribed mean curvature H satisfies a suitable condition at infinity. No smoothness assumption is required on H. We also consider the Dirichlet problem for the H-surface equation on a bounded regular domain with bounded boundary data and the H-bubble problem. Under the same assumptions on H, we prove that every weak solution is globally bounded.