To the theory of viscosity solutions for uniformly parabolic Isaacs equations

Abstract

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 $1/2$.