Regularizing effect of absorption terms in singular and degenerate elliptic problems

Abstract

In this paper we study the existence and regularity of solutions to the following singular problem \begin{equation} \left\{ \begin{array}{lll} &-\displaystyle\mbox{div} \big(a(x,u)|\nabla u|^{p-2}|\nabla u|\big) + |u|^{s-1}u =\frac{f}{u^{\gamma}} &\mbox{ in } \Omega \\ &u>0 &\mbox{ in }\Omega \\ &u=0 &\mbox{ on } \delta\Omega \end{array} \right. \end{equation} proving that the lower order term $u|u|^{s-1}$ has some regularizing effects on the solutions in the case of an elliptic operator with degenerate coercivity.