Existence results for p(x)-Laplacian equations with singular lower order terms and irregular data

This article focuses on the establishment of the existence of weak solutions for a specific class of nonlinear elliptic equations. These equations involve a singular lower order gradient term and an \(L^{1}(\Omega )\) $L^1(\mathrm{\Omega })$ datum, and they are studied within the framework of Sobolev spaces with variable exponents. Furthermore, we demonstrate that the inclusion of the lower order term has a beneficial effect on the regularity of the solutions. Specifically, it leads to a regularizing effect, enhancing the smoothness and regularity properties of the solutions.