Regularity of weak H-surfaces.

For the definition of a surface of prescribed mean curvature in a Riemannian manifold we refer the reader to S. HildebrandtH. Kaul [20]. We want to remark that the case of parametric minimal surfaces is included (H = 0 and arbitrary dimension of the target manifold). From the analytical point of view we have to deal with nonlinear elliptic Systems in all these cases. In our paper we assume the existence of so called weak Solutions of these Systems and our aim is to prove regularity results. Here the first step in regularity theory is to derive continuity of the solution. The difficulty in this case is caused by the fact that the right hand side of the equation under consideration grows quadratically in the first derivatives of the solution.

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