where N ≥ 3. We first prove a new gradient estimate for classical solutions with smooth data ρ. As a consequence we obtain that the unique weak solution of the equation satisfying a homogeneous boundary condition at infinity is locally of class W ^2,q and strictly spacelike in R^N, provided that ρ ∈ L^q(R^N)∩L^m(R^N) with q>N and m ∈ [1, 2N/(N+2)].