To the theory of viscosity solutions for uniformly parabolic Isaacs equations

Abstract

We show how a theorem about the solvability in $W_{\infty }^{1,2}$ 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 $1/2$.

22 pages, generalized results, some typos corrected, added a missing assumption which was however explicitly used. arXiv admin note: substantial text overlap with arXiv:1404.1629