The Evans-Krylov theorem for nonlocal fully nonlinear equations

Abstract

We prove a regularity result for solutions of a purely integro-differential Bellman equation. This regularity is enough for the solutions to be under-stood in the classical sense. If we let the order of the equation approach two, we recover the theorem of Evans and Krylov about the regularity of solutions to concave uniformly elliptic partial di erential equations.