Contents Online
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: https://dx.doi.org/10.4310/MAA.2015.v22.n3.a2
Author
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
Published 1 October 2015