The Dirichlet problem for graphs of prescribed anisotropic mean curvature in R~(n+1)

摘要

We consider the Dirichlet problem for graphs of prescribed mean curvature in R~(n+1) where the prescribed mean curvature function H = H(X, N) may depend on the point X in space and on the normal N of the graph as well. In some special cases this Dirichlet problem arises as the Euler equation of a generalised nonparametric area functional.