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arXiv · 1404.1629

To the theory of viscosity solutions for uniformly elliptic Isaacs equations

N. V. Krylov
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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 $C^{1+χ}$ 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 $C^γ$ with $γ$ slightly less than $1/2$.

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N. V. Krylov. 2014-04-19. To the theory of viscosity solutions for uniformly elliptic Isaacs equations. https://arxiv.org/abs/1404.1629

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