On some fractional singular elliptic systems with gradient source terms

This work studies singular nonlinear elliptic problems with gradient dependence, covering scalar equations and coupled systems. Under suitable assumptions on the data, the authors establish existence and regularity of weak solutions for arbitrary gradient growth, including the superquadratic regime, by combining new Poisson regularity estimates with a Schauder fixed-point argument.

Editorial status: Accepted for publication in Communications on Pure and Applied Analysis. No public DOI or preprint link was available at the time of this update.