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 ${x \in \varOmega \subset \mathbb {R}^n}In this article we consider the Dirichlet problem for hypersurfaces of aniso- tropic prescribed mean curvature H = H(x, u, N) depending on x ? \varOmega ì \mathbb Rⁿ{x \in \varOmega \subset \mathbb {R}^n}, the height u of the hypersurface M = graph u over \varOmega{\varOmega} and the unit normal N to M at (x, u). We give a condition relating H and the mean curvature of ?\varOmega{\partial \varOmega} that guarantees the existence of smooth solutions even for not necessarily convex domains.