We show how a theorem about the solvability in $W^{ 1,2}_{ \infty}$ of special parabolic Isaacs equations can be used to obtain the existence and uniqueness of viscosity solutions of general uniformly nondegenerate parabolic Isaacs equations. We apply it also to establish the $C^{ 1+\chi}$ 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 $C^{ \gamma}$ with respect to the spatial variables with $\gamma$ slightly less than $1/2$.
Categories: math.AP