Optimal Regularity for Fully Nonlinear Nonlocal Equations with Unbounded Source Terms

We prove optimal regularity estimates for viscosity solutions to a class of fully nonlinear nonlocal equations with unbounded source terms. More precisely, depending on the integrability of the source term \(f \in L^p(B_1)\), we establish that solutions belong to classes ranging from \(C^{\sigma-d/p}\) to \(C^\sigma\), at critical thresholds. We use approximation techniques and Liouville-type arguments. These results represent a novel contribution, providing the first such estimates in the context of not necessarily concave nonlocal equations.