In this article, we study the existence and regularity of nonnegative solutions to the following nonlinear degenerate singular elliptic equations posed on an open bounded subset \(\Omega \) of \( \mathbb {R}^N,\,N\ge 3\) : \(\begin{aligned} \left\{ \begin{aligned} -\text {div}\left( \dfrac{|\nabla z|^{p-2}\nabla z}{(1+z)^{(p-1)\tau }}\right)&=\mu \dfrac{z^s}{|x|^p}+\dfrac{f}{z^\sigma } ,\,z\ge 0 \quad \text { in } \Omega ,\\ z&=0 \quad \text { on } \partial \Omega . \end{aligned} \right. \end{aligned}\) Here \(\mu \) , \(\sigma \) , \(\tau \) and s are positive real numbers, and f is a nonnegative function that belongs to a suitable Lebesgue space. We prove that the right-hand side has a regularizing effect on the solutions, in the sense of improved summability, even though it is singular.
