A Lazer-McKenna type problem with measures

Abstract

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