Holder regularity for fully nonlinear nonlocal equations

Abstract

In this survey we prove Hölder regularity results for viscosity solutions of fully nonlinear nonlocal uniformly elliptic second order differential equations with local gradient terms. This extends the nonlocal counterpart of the work of G. Barles, E. Chasseigne and C. Imbert in JEMS, 2011, to fully nonlinear extremal nonlocal operators.