Some remarks on quasi-variational inequalities and the associated impulsive control problem

B. Perthame

Annales de l'I.H.P. Analyse non linéaire (1985)

  • Volume: 2, Issue: 3, page 237-260
  • ISSN: 0294-1449

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Perthame, B.. "Some remarks on quasi-variational inequalities and the associated impulsive control problem." Annales de l'I.H.P. Analyse non linéaire 2.3 (1985): 237-260. <http://eudml.org/doc/78098>.

@article{Perthame1985,
author = {Perthame, B.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
language = {eng},
number = {3},
pages = {237-260},
publisher = {Gauthier-Villars},
title = {Some remarks on quasi-variational inequalities and the associated impulsive control problem},
url = {http://eudml.org/doc/78098},
volume = {2},
year = {1985},
}

TY - JOUR
AU - Perthame, B.
TI - Some remarks on quasi-variational inequalities and the associated impulsive control problem
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1985
PB - Gauthier-Villars
VL - 2
IS - 3
SP - 237
EP - 260
LA - eng
UR - http://eudml.org/doc/78098
ER -

References

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  1. [1] A. Bensoussan and J.L. Lions, Nouvelle formulation de problèmes de contrôle impulsionnel et applications. Comptes Rendus, Paris, t. 276, 1973, p. 1189-1192. Zbl0266.49007MR317142
  2. [2] A. Bensoussan and J.L. Lions, Application des Inéquations variationnelles en contrôle stochastique. Dunod, 1978. Zbl0411.49002MR513618
  3. [3] A. Bensoussan and J.L. Lions, Contrôle impulsionnel et Inéquations Quasi-Variationnelles. Dunod, 1982. Zbl0491.93002MR673169
  4. [4] A. Bensoussan, J. Frehse, U. Mosco, A stochastic impulse control problem with quadratic growth Hamiltonian and the corresponding quasi-variational Inequality. J. Reine Angew. Math., t. 331, 1982, p. 124-245. Zbl0474.49013MR647377
  5. [5] L.A. Caffarelli and A. Friedman, Regularity of the solution of the quasi-variational inequality for the impulse control problem. Comm. In P. D. E., t. 3, (8), 1978, p. 745-753. Zbl0385.35010MR499353
  6. [6] L.A. Caffarelli and A. Friedman, Regularity of the solution of the Quasi-variational inequality for the impulse control problem. Comm. in P. D. E., t. 4 (3), 1979, p. 279-291. Zbl0457.35027MR522713
  7. [7] M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Zbl0599.35024
  8. [8] L.C. Evans and P.L. Lions, Resolution des équations de Hamilton-Jacobi-Bellman pour les équations uniformément elliptiques. C. R. A. S., t. 290, 1980, p. 1049-1052. Zbl0461.49017MR582494
  9. [9] J. Frehse and U. Mosco, Irregular obstacles and quasi-Variational Inequalities of Stochastic Impulse Control. Annali di Pisa, t. 4, 91, 1982, p. 105-157. Zbl0503.49008MR664105
  10. [10] B. Hanouzet and J.L. Joly, Convergence uniforme des itérés définissant la solution faible d'une Inéquation Quasi-variationnelle. C. R. A. S., t. 286, 1978, p. 735-738. Zbl0373.49012MR496035
  11. [11] S. Lehnart, Bellman equations for Optimal stopping time problems. Indiana U. Math. J., t. 32, 3, 1983, p. 363-375. Zbl0487.49014
  12. [12] P.L. Lions, Resolution Analytique des Problèmes des Bellman Dirichlet. Acta Mathematica, t. 146, 1981, p. 151-166. Zbl0467.49016MR611381
  13. [13] P.L. Lions, Optimal control and Hamilton-Jacobi-Bellman equations. Part 2, Viscosity solutions and uniqueness. Comm. in P. D. E., t. 8, 1983, p. 1101-1174. Zbl0716.49022
  14. [14] P.L. Lions, Optimal control and Hamilton-Jacobi-Bellman equations. Part. 3. Regularity of the optimal cost function. In Non-linear partial differential equations and applications, Collège de France, Seminar, Vol. V, Pitman, London, 1983. Zbl0716.49024
  15. [15] K. Miller, Barriers on cones for uniformly elliptic operators. Annali diMathematica, t. 2, 76, 1967, p. 93-105. Zbl0149.32101MR221087
  16. [16] B. Perthame, Quasi-Variational Inequalities and Hamilton-Jacobi-Bellman Equations in a bounded region. Comm. in P. D. E., t. 9, 6, 1984, p. 561-595. MR742509
  17. [17] B. Perthame, Continuous and Impulsive control of diffusion in RN. Non Linear Analysis T. M. A., t. 8, 10, 1984, p. 1227-1239. Zbl0513.93068MR763660
  18. [18] B. Perthame. On the regularity of the solutions of Quasi-Variational Inequalities. To appear. 

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