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Abstract

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