JournalsrlmVol. 18 , No. 3DOI 10.4171/rlm/490

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

  • Roberta Musina

    Università di Udine, Italy
On the regularity of weak solutions to <em>H</em>-systems cover

Abstract

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