  We investigate the differences and similarities of the Dirichlet problem of
the mean curvature equation in the Euclidean space and in the Lorentz-Minkowski
space. Although the solvability of the Dirichlet problem follows standards
techniques of elliptic equations, we focus in showing how the spacelike
condition in the Lorentz-Minkowski space allows to drop the hypothesis on the
mean convexity which is required in the Euclidean case.
