  In this paper we provide a complete characterization of the regularity
properties of the solutions associated to the homogeneous Dirichlet problem
\begin{equation*}
  \begin{cases}
  \displaystyle - \Delta_1 u= h(u)f & \text{in } \Omega, \\ \newline
  u=0 & \text{on } \partial \Omega,
  \end{cases} \end{equation*} where $\Omega\subset\mathbb{R}^N$ is a bounded
open set with Lipschitz boundary, $f \in L^m(\Omega)$ with $m\geq 1$ is a
nonnegative function and $h\colon \mathbb{R}^+ \to \mathbb{R}^+$ is continuous,
possibly singular at the origin and bounded at infinity.
  Without any growth restrictions on $h$ at zero, we prove existence of global
finite energy solutions in $BV(\Omega)$ under sharp conditions on the
summability of $f$ and on the behaviour of $h$ at infinity. Roughly speaking,
the faster $h$ goes to zero at infinity, the less regularity is required on
$f$. In contrast to the $p$-Laplacian case ($p>1$), we show that the behaviour
of $h$ at the origin plays essentially no role.
  The main result contains an extension of the celebrated one of Lazer-McKenna
(\cite{lm}) to the case of the $1$-Laplacian as principal operator.
