JournalsrlmVol. 18, No. 3pp. 209–219

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
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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.

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. 209–219

DOI 10.4171/RLM/490