A Lazer-McKenna type problem with measures

In this paper we are concerned with a general singular Dirichlet boundary value problem whose model is the following $$\{\begin{array}{llll}-\mathrm{\Delta }u=\frac{\mu }{u^{\gamma }}& \text{in }\mathrm{\Omega },u=0& \text{on }\mathrm{\partial }\mathrm{\Omega },u>0& \text{on }\mathrm{\Omega }\mathrm{.}\end{array}$$ Here $\mu$ is a nonnegative bounded Radon measure on a bounded open set $\mathrm{\Omega }\subset {\mathbb{R}}^N$, and $\gamma >0$.