On a class of graphs with prescribed mean curvature (Q1325179)

The authors consider equations of the form \(\sum^ n_{j=1} D_ j \{G(| x |^ 2\), \(| Du |^ 2) D_ ju\} = H(| x|)\) on the unit ball in \(\mathbb{R}^ n\). Using a barrier-function technique they establish boundary estimates, a maximum principle for the gradient, and a global gradient estimate. A consequence is that solutions having constant boundary values have to be radial. Moreover, these results can be applied to graphs with prescribed mean curvature defined on hyperbolic \(n\)-space.