To the theory of viscosity solutions for uniformly parabolic Isaacs equations

2014/05/04 by N. V. Krylov, Krylov, N. V.
Mathematics · #35B65 #35K55 #65N15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1405.0633

openalex publication_date 2014/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show how a theorem about the solvability in W^1,2_∞ 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+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 respect to the spatial variables with γ slightly less than 1/2.

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