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Differential Games and Directional Derivatives of Viscosity Solutions of Isaacs’ Equations II

Lions, Pierre-Louis; Souganidis, Panagiotis E. (1986), Differential Games and Directional Derivatives of Viscosity Solutions of Isaacs’ Equations II, SIAM Journal on Control and Optimization, 24, 5, p. 1086-1089. http://dx.doi.org/10.1137/0324065

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Type
Article accepté pour publication ou publié
Date
1986
Journal name
SIAM Journal on Control and Optimization
Volume
24
Number
5
Publisher
SIAM
Pages
1086-1089
Publication identifier
Metadata
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Author(s)
Lions, Pierre-Louis
Souganidis, Panagiotis E.
Abstract (EN)
Recent work by the authors [this Journal, 23 (1985), pp. 566-583], has demonstrated the con-nections between the notion of viscosity sub- and super-solutions of first-order, dynamic programming PDE and the optimality principle of dynamic programming, as well as the directional derivatives of viscosity solutions of the above equations at an arbitrary point. The present note contains a remark and a counterexample which complement the results cited.
Subjects / Keywords
differential games; optimal control; Hamilton–Jacobi equations; directional derivatives; viscosity solutions