Characterizations of the values of differential games
type: Item
instance of: scholarly article
title: Characterizations of the values of differential games
zbMATH Open document ID: 0647.90108
DOI: 10.1007/BF01448365
author: Leonard David Berkovitz
published in: Applied Mathematics and Optimization
publication date: 1988-01-01T00:00:00Z
review text: Differential games with most general payoffs are considered. It is shown that under some assumptions the upper and lower directional derivatives of the value functions of such differential games satisfy certain relationships. At points of differentiability of the value functions these relationships reduce to the Isaacs equation. As it was shown earlier these relationships imply that the value is a viscosity solution of the Isaacs equation.
reviewed by: G.Yu.Garnaeva
Mathematics Subject Classification ID: 91A23
zbMATH DE Number: 4057331
zbMATH Keywords: most general payoffs
zbMATH Keywords: upper and lower directional derivatives of the value functions
zbMATH Keywords: Isaacs equation
zbMATH Keywords: viscosity solution
MaRDI profile type: Publication
cites work: Viscosity solutions of Isaacs' equations and differential games with Lipschitz controls
cites work: The Existence of Value and Saddle Point in Games of Fixed Duration
cites work: Differential Games of Generalized Pursuit and Evasion
cites work: Q3396313
cites work: Q5510093
cites work: Q5638152
cites work: Q4404710
cites work: Q3344757
cites work: Differential Games, Optimal Control and Directional Derivatives of Viscosity Solutions of Bellman’s and Isaacs’ Equations
cites work: Generalization of the main equation of differential game theory
description: scientific article; zbMATH DE number 4057331