C sigma+alfa regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels

Abstract

We establish Cs+a interior estimates for concave nonlocal fully nonlinear equations of order s¿(0,2) with rough kernels. Namely, we prove that if u¿Ca(Rn) solves in B1 a concave translation invariant equation with kernels in L0(s), then u belongs to (Formula Presented), with an estimate. More generally, our results allow the equation to depend on x in a Ca fashion. Our method of proof combines a Liouville theorem and a blow-up (compactness) procedure. Due to its flexibility, the same method can be useful in different regularity proofs for nonlocal equations.