  In this paper, we study the static Born-Infeld equation $$
-\mathrm{div}\left(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\right)=\sum_{k=1}^n
a_k\delta_{x_k}\quad\mbox{in }\mathbb R^N,\qquad \lim_{|x|\to\infty}u(x)=0, $$
where $N\ge3$, $a_k\in\mathbb R$ for all $k=1,\dots,n$, $x_k\in\mathbb R^N$ are
the positions of the point charges, possibly non symmetrically distributed, and
$\delta_{x_k}$ is the Dirac delta distribution centered at $x_k$. For this
problem, we give explicit quantitative sufficient conditions on $a_k$ and $x_k$
to guarantee that the minimizer of the energy functional associated to the
problem solves the associated Euler-Lagrange equation. Furthermore, we provide
a more rigorous proof of some previous results on the nature of the
singularities of the minimizer at the points $x_k$'s depending on the sign of
charges $a_k$'s. For every $m\in\mathbb N$, we also consider the approximated
problem $$ -\sum_{h=1}^m\alpha_h\Delta_{2h}u=\sum_{k=1}^n
a_k\delta_{x_k}\quad\mbox{in }\mathbb R^N, \qquad\lim_{|x|\to\infty}u(x)=0 $$
where the differential operator is replaced by its Taylor expansion of order
$2m$, see (2.1). It is known that each of these problems has a unique solution.
We study the regularity of the approximating solution, the nature of its
singularities, and the asymptotic behavior of the solution and of its gradient
near the singularities.
