  We consider a Dirichlet problem for the mean curvature operator in the
Minkowski spacetime, obtaining a necessary and sufficient condition for the
existence of a spacelike solution, with prescribed mean curvature, which is the
graph of a function defined on a domain equal to the complement in $\mathbb
R^n$ of the union of a finite number of bounded Lipschitz domains. The mean
curvature $H=H(x,t)$ is assumed to have absolute value controlled from above by
a locally bounded, $L^p$-function, $p\in [1,2n/(n+2)]$, $n\geq 3$.
