1-Laplacian type problems with strongly singular nonlinearities and gradient terms

We show optimal existence, nonexistence and regularity results for nonnegative solutions to Dirichlet problems as $$ \begin{cases} \displaystyle -\Delta_1 u = g(u)|D u|+h(u)f & \text{in}\;\Omega,\\ u=0 \text{on}\;\partial\Omega, \end{cases} where $\Omega$ is an open bounded subset of $\mathbb{R}^N$, $f\geq 0$ belongs $L^N(\Omega)$, $g$ $h$ are continuous functions that may blow up at zero. As a noteworthy fact we how non-trivial interaction mechanism between the two nonlinearities produces remarkable regularizing effects on solutions. The sharpness our main discussed through use appropriate explicit examples.