Viability and invariance for differential games with applications to Hamilton-Jacobi-Isaacs equations
Pierre Cardaliaguet; Sławomir Plaskacz
Banach Center Publications (1996)
- Volume: 35, Issue: 1, page 149-158
- ISSN: 0137-6934
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top- [1] J.-P. Aubin, Viability Theory, Birkhäuser, Boston, Basel, Berlin (1991).
- [2] J.-P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag (1984). Zbl0538.34007
- [3] J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, Basel, Berlin (1990).
- [4] P. Cardaliaguet, Domaines discriminant en jeux différentiels, Ph.D. Thesis, Université Paris Dauphine (1992).
- [5] M. G. Crandall, L. C. Evans and P. L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 282, 487-502. Zbl0543.35011
- [6] M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-42.
- [7] R. J. Elliott and N. J. Kalton, The existence of value in differential games, Mem. Amer. Math. Soc. 126 (1972). Zbl0244.90046
- [8] L. C. Evans and P. E. Souganidis, Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations, Indiana Univ. Math. J. 33 (1984), 773-797. Zbl1169.91317
- [9] H. Frankowska, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations, SIAM J. Control And Optimization 31 (1993), 257-272. Zbl0796.49024
- [10] H. Frankowska and S. Plaskacz, A measurable - upper semicontinuous viability theorem for tubes, Nonlinear Analysis TMA. (to appear). Zbl0838.34017
- [11] H. Frankowska, S. Plaskacz and T. Rzeżuchowski, Théorèmes de viabilité mesurables et l'équation d'Hamilton-Jacobi-Bellman, Comptes-Rendus de l'Académie des Sciences, Paris, Série 1 (1992).
- [12] H. Frankowska, S. Plaskacz and T. Rzeżuchowski, Measurable viability theorems and Hamilton-Jacobi-Bellman equation, J. Diff. Eqs. 116 (1995), 265-305. Zbl0836.34016
- [13] R. T. Rockafellar, Proximal subgradients, marginal values, and augmented Lagrangians in nonconvex optimization, Math. of Oper. Res. 6 (1981), 424-436. Zbl0492.90073
- [14] E. Roxin, The axiomatic approach in differential games, J. Optim. Theory Appl. 3 (1969), 153-163. Zbl0175.10504
- [15] P. P. Varaiya, The existence of solutions to a diffrential game, SIAM J. Control Optim. 5 (1967), 153-162. Zbl0154.09901