To the theory of viscosity solutions for uniformly elliptic Isaacs equations

We show how a theorem about the solvability in C1,1 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 C1+χ regularity of viscosity solutions and show that finite-dif...

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Bibliographic Details
Published in:Journal of functional analysis 2014-12, Vol.267 (11), p.4321-4340
Main Author: Krylov, N.V.
Format: Article
Language:English
Subjects:
Finite-difference approximations
Fully nonlinear equations
Hölder regularity of derivatives
Viscosity solutions
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Summary:We show how a theorem about the solvability in C1,1 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 C1+χ 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 Cγ with γ slightly less than 1/2.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2014.09.026