To the theory of viscosity solutions for uniformly elliptic Isaacs equations

2014/04/06 by Krylov, N. V.
#35D40 #35J60 #39A14 #49N70 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1404.1629

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.

Related

• To the theory of viscosity solutions for uniformly parabolic Isaacs equations
• On the rate of convergence of finite-difference approximations for elliptic Isaacs equations in smooth domains
• Regularity theory for the Isaacs equation through approximation methods
• Uniqueness for L_p-viscosity solutions for uniformly parabolic Isaacs equations with measurable lower order terms
• Regularity properties for a class of non-uniformly elliptic Isaacs operators