Remark on the anisotropic prescribed mean curvature equation on arbitrary domains

In this article we consider the Dirichlet problem for hypersurfaces of aniso- tropic prescribed mean curvature H = H ( x , u , N ) depending on , the height u of the hypersurface M = graph u over and the unit normal N to M at ( x , u ). We give a condition relating H and the mean curvature of that guarantees the existence of smooth solutions even for not necessarily convex domains.