Geodesic
Existence of solutions with singularities for the~maximal surface equation in Minkowski space
Sbornik. Mathematics, Tome 80 (1995) no. 1, pp. 87-104

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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 $a_i$. 
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     author = {A. A. Klyachin and V. M. Miklyukov},
     title = {Existence of solutions with singularities for the~maximal surface equation in {Minkowski} space},
     journal = {Sbornik. Mathematics},
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     number = {1},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_80_1_a4/}
}
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A. A. Klyachin; V. M. Miklyukov. Existence of solutions with singularities for the~maximal surface equation in Minkowski space. Sbornik. Mathematics, Tome 80 (1995) no. 1, pp. 87-104. http://geodesic.mathdoc.fr/item/SM_1995_80_1_a4/