To the theory of viscosity solutions for uniformly elliptic Isaacs equations

N. V. Krylov

doi:10.1016/j.jfa.2014.09.026

To the theory of viscosity solutions for uniformly elliptic Isaacs equations

N. V. Krylov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We show how a theorem about the 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.

Original language	English (US)
Pages (from-to)	4321-4340
Number of pages	20
Journal	Journal of Functional Analysis
Volume	267
Issue number	11
DOIs	https://doi.org/10.1016/j.jfa.2014.09.026
State	Published - Dec 1 2014

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.

Keywords

Finite-difference approximations
Fully nonlinear equations
Hölder regularity of derivatives
Viscosity solutions

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10.1016/j.jfa.2014.09.026

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abstract = "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.",

keywords = "Finite-difference approximations, Fully nonlinear equations, H{\"o}lder regularity of derivatives, Viscosity solutions",

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N2 - 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.

AB - 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.

KW - Finite-difference approximations

KW - Fully nonlinear equations

KW - Hölder regularity of derivatives

KW - Viscosity solutions

UR - https://www.scopus.com/pages/publications/84908191747

UR - https://www.scopus.com/pages/publications/84908191747#tab=citedBy

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DO - 10.1016/j.jfa.2014.09.026

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VL - 267

SP - 4321

EP - 4340

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 11

ER -

To the theory of viscosity solutions for uniformly elliptic Isaacs equations

Abstract

Bibliographical note

Keywords

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