Existence of solutions with singularities for the maximal surface equation in Minkowski space

Let $\Omega$ be a domain in $\mathbb{R}^n$, and $A=(a_1,\dots,a_N)$ a finite tuple of points in $\Omega$. The problem is considered of the existence of a solution for the maximal surface equation in $\Omega\setminus A$, where Dirichlet boundary data are given on $\partial\Omega$, and the flows of the time gradient on the graph of the solution in the Minkowski space $\mathbb{R}_1^{n+1}$ are given at the points $a_i$.