Methods and Applications of Analysis

Volume 22 (2015)

Number 3

To the theory of viscosity solutions for uniformly parabolic Isaacs equations

Pages: 259 – 280

DOI: http://dx.doi.org/10.4310/MAA.2015.v22.n3.a2

Author

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

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 $1/2$.

Keywords

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

2010 Mathematics Subject Classification

35B65, 35K55, 65N15

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Published 1 October 2015