On the Regularizing Effect of Some Absorption and Singular Lower Order Terms in Classical Dirichlet Problems with L1 Data

Abstract

We are interested in existence and regularity results concerning the solution to the following problem $$\left\{ \begin{array}{l} - \Delta u + {u^8} = \frac{{f\left( x \right)}}{{{u^\gamma }}}in\,\Omega \\ u > 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,in\,\Omega \\ u = 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,on\,\partial \Omega \\ \end{array} \right.\, $$