Regularity for Fully Nonlinear Equations Driven by Spatial-Inhomogeneous Nonlocal Operators

摘要

We consider a class of nonlocal operators that are not necessarily spatially homogeneous and impose mild assumptions on its kernel near zero. Furthermore, we prove Holder regularity for a large class of fully nonlinear integro-differential equations. In particular, the results cover the case when the kernel K(x,y) is comparable to for |x-y|< r (0), where 0 < alpha < 2.