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The Evans-Krylov theorem for nonlocal fully nonlinear equations. (English) Zbl 1232.49043
Summary: We prove a regularity result for solutions of a purely integro-differential Bellman equation. This regularity is enough for the solutions to be understood 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 differential equations.

MSC:
49N60 Regularity of solutions in optimal control
49L20 Dynamic programming in optimal control and differential games
35J65 Nonlinear boundary value problems for linear elliptic equations
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