Methods and Applications of Analysis

Volume 22 (2015)

Number 3

To the theory of viscosity solutions for uniformly parabolic Isaacs equations

Pages: 259 – 280



N. V. Krylov (School of Mathematics, University of Minnesota, Minneapolis, Minn., U.S.A.)


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 $1/2$.


fully nonlinear equations, viscosity solutions, Hölder regularity of derivatives, numerical approximation rates

2010 Mathematics Subject Classification

35B65, 35K55, 65N15

Published 1 October 2015