Spacelike graphs with prescribed mean curvature on exterior domains in the Minkowski spacetime

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