To the theory of viscosity solutions for uniformly elliptic Isaacs equations

Abstract

We show how a theorem about solvability in $C^{1,1}$ 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 $C^{1+\chi }$ 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 $\gamma$ slightly less than $1/2$.

17 pages, better references, better statements about the dependence of constants on the data

References in corpus (2)

• Error estimates for approximations of nonhomogeneous nonlinear uniformly elliptic equations
• Error estimates for approximations of nonlinear uniformly parabolic equations