Nonlocal Liouville Theorems with Gradient Nonlinearity

In this article we consider a large family of nonlinear nonlocal equations involving gradient nonlinearity and provide a unified approach, based on the Ishii-Lions type technique, to establish Liouville properties of the solutions. We also answer an open problem raised by Cirant and Goffi [24]. Some applications to regularity issues are also studied. © 2025 Elsevier Inc.