To the theory of viscosity solutions for uniformly elliptic Isaacs equations

We show how a theorem about the solvability in C1,1C1,1 of special Isaacs equations can be used to obtain existence and uniqueness of viscosity solutions of general uniformly nondegenerate Isaacs equations. We apply it also to establish the C1+χC1+χ regularity of viscosity solutions and show that finite-difference approximations have an algebraic rate of convergence. The main coefficients of the Isaacs equations are supposed to be in CγCγ with γ slightly less than 1/2.