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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Cardaliaguet, Pierre, and Plaskacz, Sławomir. "Viability and invariance for differential games with applications to Hamilton-Jacobi-Isaacs equations." Banach Center Publications 35.1 (1996): 149-158. <http://eudml.org/doc/251344>.

@article{Cardaliaguet1996,
author = {Cardaliaguet, Pierre, Plaskacz, Sławomir},
journal = {Banach Center Publications},
keywords = {viscosity solutions; Hamilton-Jacobi equations; Isaacs equation},
language = {eng},
number = {1},
pages = {149-158},
title = {Viability and invariance for differential games with applications to Hamilton-Jacobi-Isaacs equations},
url = {http://eudml.org/doc/251344},
volume = {35},
year = {1996},
}

TY - JOUR
AU - Cardaliaguet, Pierre
AU - Plaskacz, Sławomir
TI - Viability and invariance for differential games with applications to Hamilton-Jacobi-Isaacs equations
JO - Banach Center Publications
PY - 1996
VL - 35
IS - 1
SP - 149
EP - 158
LA - eng
KW - viscosity solutions; Hamilton-Jacobi equations; Isaacs equation
UR - http://eudml.org/doc/251344
ER -

References

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  1. [1] J.-P. Aubin, Viability Theory, Birkhäuser, Boston, Basel, Berlin (1991). 
  2. [2] J.-P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag (1984). Zbl0538.34007
  3. [3] J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, Basel, Berlin (1990). 
  4. [4] P. Cardaliaguet, Domaines discriminant en jeux différentiels, Ph.D. Thesis, Université Paris Dauphine (1992). 
  5. [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. [6] M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-42. 
  7. [7] R. J. Elliott and N. J. Kalton, The existence of value in differential games, Mem. Amer. Math. Soc. 126 (1972). Zbl0244.90046
  8. [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. [9] H. Frankowska, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations, SIAM J. Control And Optimization 31 (1993), 257-272. Zbl0796.49024
  10. [10] H. Frankowska and S. Plaskacz, A measurable - upper semicontinuous viability theorem for tubes, Nonlinear Analysis TMA. (to appear). Zbl0838.34017
  11. [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. [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. [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. [14] E. Roxin, The axiomatic approach in differential games, J. Optim. Theory Appl. 3 (1969), 153-163. Zbl0175.10504
  15. [15] P. P. Varaiya, The existence of solutions to a diffrential game, SIAM J. Control Optim. 5 (1967), 153-162. Zbl0154.09901

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