An impulsive control problem with state constraint

P. L. Lions; B. Perthame

Annales de l'I.H.P. Analyse non linéaire (1989)

  • Volume: S6, page 385-414
  • ISSN: 0294-1449

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Lions, P. L., and Perthame, B.. "An impulsive control problem with state constraint." Annales de l'I.H.P. Analyse non linéaire S6 (1989): 385-414. <http://eudml.org/doc/78204>.

@article{Lions1989,
author = {Lions, P. L., Perthame, B.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {impulsive control problem; state constraints; weak solution},
language = {eng},
pages = {385-414},
publisher = {Gauthier-Villars},
title = {An impulsive control problem with state constraint},
url = {http://eudml.org/doc/78204},
volume = {S6},
year = {1989},
}

TY - JOUR
AU - Lions, P. L.
AU - Perthame, B.
TI - An impulsive control problem with state constraint
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1989
PB - Gauthier-Villars
VL - S6
SP - 385
EP - 414
LA - eng
KW - impulsive control problem; state constraints; weak solution
UR - http://eudml.org/doc/78204
ER -

References

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  1. [1 ] A. Bensoussan and J.L. Lions. Nouvelle formulation de problèmes de contrôle impulsionnel et applications. C.R. Ac. Sc. Paris276 (1973), pp. 1189-1192. Zbl0266.49007MR317142
  2. [2 ] A. Bensoussan and J.L. Lions. Applications des Inéquations Variationnelles en contrôle stochastique. Dunod, Paris, 1978. Zbl0411.49002MR513618
  3. [3 ] A. Bensoussan and J.L. Lions. Contrôle Impulsionnel et Inéquations Quasi-Variationnelles. Dunod, Paris, 1982. Zbl0491.93002MR673169
  4. [4 ] L.A. Caffarelli and A. Friedman. Regularity of the solutions of the quasi-variational inequality for the impulse control. I, Comm. in P.D.E., 3 (8), (1978), pp. 745-753. II. Comm. in P.D.E., 4 (3), (1979), pp. 279-291. Zbl0385.35010
  5. [5 ] M.G. Crandall and P.L. Lions. Viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc.277 (1983), pp. 1-42. Zbl0599.35024MR690039
  6. [6 ] L.C. EvansClassical solutions of the Hamilton-Jacobi-Bellman equation for uniformly elliptic operators. Trans. Amer, Math, Soc.275 (1983), pp. 245-255. MR678347
  7. [7 ] L.C. Evans and P.L. Lions, Résolution des equations de Hamilton-Jacobi-Bellman pour les opérateurs uniformément elliptiques. C.R. Acad. Sc. Paris, t 290, (1980), pp. 1049-1052. Zbl0461.49017MR582494
  8. [8 ] B. Hanouzet and J.L. Joly. Convergence uniforme des itérés définissant la solution faible d'une Inéquation Quasi-Variationnelle. C.R. Acd. Sc. Paris, 286 (1978), pp. 735-738. Zbl0373.49012MR496035
  9. [9 ] R. JensenBoundary Regularity for Variational Inequalities. Indiana Univ. Math. J., 29 (1980), pp. 495-504. Zbl0469.49008MR578201
  10. [10 ] N.V. KrylovControlled Diffusion Process. Springer-Verlag, Berlin, (1980). Zbl0459.93002MR601776
  11. [11 ] S. LenhartBellman equations for optimal stopping time problems. Indiana Univ. Math. J., 32 (3), (1983), pp. 363-375. Zbl0487.49014MR697642
  12. [12 ] P.L. LionsControlled Diffusion process in IRN . Comm. Pure Appl. Math., 34 (1981), pp. 121-147. Zbl0441.49020
  13. [13 ] P.L. LionsRésolution analytique des problèmes de Bellman-Dirichlet. Acta Mathematica, t. 146, (1981), pp. 363-375. Zbl0467.49016MR611381
  14. [14 ] P.L. LionsOptimal control and Hamilton-Jacobi-Bellman equations, Part 1,2, Comm. in P.D.E.8 (1983), pp. 1101-1174, pp. 1229-1276. Part 3 : Regularity of the optimal cost function, in "Nonlinear Partial Differential Equations and Applications", Collège de France Seminar, Vol. V, Pitman, London, (1983). Zbl0716.49022
  15. [15 ] B. PerthameQuasi-Variational Inequalities and Hamilton-Jacobi Equations in a bounded region, Comm. in P.D.E., 9 (6), (1984), pp. 561-595. 
  16. [16 ] B. PerthameSome remarks on Q.V.I, and the associated impulsive control problem. Ann. Inst. H. Poincaré, Vol. 2, n°3, (1985), pp. 237-260. MR797272
  17. [17 ] B. PerthameOn the regularity of the solutions of Q.V.I., J. of Funct. Anal., 64 (2), (1985), pp. 190-208. MR812391
  18. [18 ] B. PerthameContinuous and impulsive control of diffusion in RN . Non-linear Analyse T.M.A., t.8, 10 (1984), pp, 1227-1239. Zbl0513.93068MR763660

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