In this paper we prove that every weak solution to the -surface equation is locally bounded, provided the prescribed mean curvature satisfies a suitable condition at infinity. No smoothness assumption is required on . We consider also the Dirichlet problem for the -surface equation on a bounded regular domain with boundary data and the -bubble problem. Under the same assumptions on , we prove that every weak solution is globally bounded.
Cite this article
Roberta Musina, On the regularity of weak solutions to <em>H</em>-systems. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 3, pp. 209–219DOI 10.4171/RLM/490