Solutions de viscosité des équations de Hamilton-Jacobi du premier ordre et applications

P-L. Lions

Séminaire Équations aux dérivées partielles (Polytechnique) (1983-1984)

  • page 1-12

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Lions, P-L.. "Solutions de viscosité des équations de Hamilton-Jacobi du premier ordre et applications." Séminaire Équations aux dérivées partielles (Polytechnique) (1983-1984): 1-12. <http://eudml.org/doc/111858>.

@article{Lions1983-1984,
author = {Lions, P-L.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {survey; viscosity solutions; first order Hamilton-Jacobi equations; existence; uniqueness; deterministic optimal control; asymptotic problems},
language = {fre},
pages = {1-12},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Solutions de viscosité des équations de Hamilton-Jacobi du premier ordre et applications},
url = {http://eudml.org/doc/111858},
year = {1983-1984},
}

TY - JOUR
AU - Lions, P-L.
TI - Solutions de viscosité des équations de Hamilton-Jacobi du premier ordre et applications
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1983-1984
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 12
LA - fre
KW - survey; viscosity solutions; first order Hamilton-Jacobi equations; existence; uniqueness; deterministic optimal control; asymptotic problems
UR - http://eudml.org/doc/111858
ER -

References

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  1. [1] G. Barles: Existence results for first order Hamilton-Jacobi equations. In These 3e cycle, Univ. Paris IX-Daphine, 1983. A paraître dans Trans. Amer. Math. Soc. Zbl0574.70019
  2. [2] E.N. Barron, L.C. Evans et R. Jensen: Viscosity solutions of Isaac's equations and differential games with Lipschitz controls. A paraître dans J. Diff. Eq. Zbl0548.90104
  3. [3] M.G. Grandall, L.C. Evans et P-L. Lions: Some properties of viscosity solutions of Hamilton-Jacobi equations. A paraître dans Trans. Amer. Math.Soc Zbl0543.35011
  4. [4] M.G. Grandall et P-L. Lions: Conditions d'unicité pour les solutions généralisées des équations de Hamilton-Jacobi du premier ordre: C.R.A.S.Paris, 292 (1981), p. 183-186. Zbl0469.49023MR610314
  5. [5] M.G. Grandall et P-L. Lions: Viscosity solutions of Mamilton-Jacobi equations. Trans. Amer. Math. Soc., 277 (1983), p. 1-42. Zbl0599.35024MR690039
  6. [6] M.G. Grandall et P.L. Lions: Solutions de viscosité non bornées des équations de Hamilton-Jacobi du premier ordre. C.R.A.S.Paris1984; et article détaillé en préparation. Zbl0565.49022
  7. [7] M.G. Grandall et P-L. Lions: Two approximations of solutions of Hamilton-Jacobi equations. Maths. Comp., à paraître. Zbl0556.65076
  8. [8] L.C. Evans et P.E. Souganidis: Differential games and representations formulas for solutions of Hamilton-Jacobi-Isaacs equations. MRC Report #2452, Univ. of Wisconsin- Madison, 1983. MR756158
  9. [9 ] W.H. Fleming: The Cauchy problem for degenerate parabolic equations. J. Math. Mech., 13 (1964), p. 987-1008. Zbl0192.19602MR179473
  10. [10] W.H. Fleming: The Cauchy problem for a nonlinear first order partial differential equation. J. Diff. Eq., 5 (1969), p. 515-530. Zbl0172.13901MR235269
  11. [11] A. Friedman: The Cauchy problem for first order partial dif f erential equationsInd. Univ. Math. J., 23, (1973), p. 27-40. Zbl0243.35014MR326136
  12. [12] D. Gilbarg et N.S. Trudinger: Elliptic partial differential equations of second order. Springer, Berlin, 1977. Zbl1042.35002MR473443
  13. [13] H. Ishii; Uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations. Preprint. Zbl0551.49016MR756156
  14. [14] S.N. Kružkov: Generalized solutions of nonlinear first order equations and of several variables. I, Mat. Sb., 70(112) (1966), p. 394-415; II, Math. USSR Sbornik, 1 (1967), p. 93-116. Zbl0164.40802MR199543
  15. [15] S.N. Kružkov: Generalized solutions of the Hamilton-Jacobi equations of Eikonal type. I, Math. USSR Sbornik, 27 (1975), p. 406 - 446. Zbl0369.35012
  16. [16] O.A. Ladyzenskaya et N.N. Ural'tseva: Linear and quasilinear elliptic equations. Academic Press, New-York, 1968. Zbl0164.13002MR244627
  17. [17] P-L. Lions: Generalized solutions of Hamilton-Jacobi equations. Pitman, Londres, 1982. Zbl0497.35001MR667669
  18. [18] P-L. Lions: Existence results for first order Hamilton-Jacobi equations. Ric. Mat., 1983. Zbl0552.70012MR740198
  19. [19] P-L. Lions: Résolution de problèmes quasilinéaires. Arch. Rat. Mech. Anal., 74 (1980), p. 335-354. Zbl0449.35036MR588033
  20. [20] P-L. Lions et M. Nisio: A uniqueness result for the semigroup associated with the Hamilton-Jacobi-Bellman operator. Proc. Japan Acad., 58 (1982), p. 273-276. Zbl0516.93065MR682680
  21. [21] P-L. Lions, G. Papanicolaou et S.R.S. Varadhan: travail en préparation. 
  22. [22] J. Serrin: The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables. Philos.Trans.Roy. Soc, London. Ser. A, 264 (1969), p. 413-496. Zbl0181.38003MR282058
  23. [23] P.E. Souganidis: Existence of viscosity solutions of Hamilton-Jacobi equations. J. Diff. Eq., à paraître. Zbl0506.35020
  24. [24] P.E. Souganidis: Thesis, Univ. of Wisconsin -Madison, 1983. 

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