On the regularity of weak solutions to <em>H</em>-systems

Abstract

In this paper 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 consider also the Dirichlet problem for the $H$-surface equation on a bounded regular domain with $L^{\infty}$ boundary data and the $H$-bubble problem. Under the same assumptions on $H$, we prove that every weak solution is globally bounded.