  We construct geometric barriers for minimal graphs in H^n xR. We prove the
existence and uniqueness of a solution of the vertical minimal equation in the
interior of a convex polyhedron in H^n extending continuously to the interior
of each face, taking infinite boundary data on one face and zero boundary value
data on the other faces. In H^n xR, we solve the Dirichlet problem for the
vertical minimal equation in a C^0 convex domain taking arbitrarily continuous
finite boundary and asymptotic boundary data. We prove the existence of another
Scherk type hypersurface, given by the solution of the vertical minimal
equation in the interior of certain admissible polyhedron taking alternatively
infinite values +\infty and -\infty on adjacent faces of this polyhedron. Those
polyhedra may be chosen convex or non convex. We establish analogous results
for minimal graphs when the ambient is the Euclidean space R^ {n+1}.
