EXISTENCE OF SOLUTIONS WITH SINGULARITIES FOR THE MAXIMAL SURFACE EQUATION IN MINKOWSKI SPACE

Let Omega be a domain in R(n), and A = (a(1),..., 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 \ A, where Dirichlet boundary data are given on partial derivative Omega, and the flows of the time gradient on the graph of the solution in the Minkowski space R(1)(n+1) are given at the points a(i).