An approach of deterministic control problems with unbounded data

G. Barles

Annales de l'I.H.P. Analyse non linéaire (1990)

  • Volume: 7, Issue: 4, page 235-258
  • ISSN: 0294-1449

How to cite

top

Barles, G.. "An approach of deterministic control problems with unbounded data." Annales de l'I.H.P. Analyse non linéaire 7.4 (1990): 235-258. <http://eudml.org/doc/78222>.

@article{Barles1990,
author = {Barles, G.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {comparison results; deterministic unbounded control problem; maximum viscosity subsolution; Bellman equations; Hamilton-Jacobi equation; gradient constraints; uniqueness; nonconvex},
language = {eng},
number = {4},
pages = {235-258},
publisher = {Gauthier-Villars},
title = {An approach of deterministic control problems with unbounded data},
url = {http://eudml.org/doc/78222},
volume = {7},
year = {1990},
}

TY - JOUR
AU - Barles, G.
TI - An approach of deterministic control problems with unbounded data
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1990
PB - Gauthier-Villars
VL - 7
IS - 4
SP - 235
EP - 258
LA - eng
KW - comparison results; deterministic unbounded control problem; maximum viscosity subsolution; Bellman equations; Hamilton-Jacobi equation; gradient constraints; uniqueness; nonconvex
UR - http://eudml.org/doc/78222
ER -

References

top
  1. [1] G. Barles, Quasi-variational inequalities and first-order Hamilton-Jacobi Equations. Non lin. Anal. TMA, vol. 9, n° 2, 1985. Zbl0637.49014
  2. [2] G. Barles, Existence results for first-order and Hamilton-Jacobi Equations. Ann. I. H. P., Anal. non lin., vol. 1, t. 5, 1984. Zbl0574.70019MR779871
  3. [3] G. Barles, Remarks on existence results for first-order Hamilton-Jacobi Equations. Ann. I. H. P., Anal. non lin., t. 2, 1985. Zbl0573.35010MR781590
  4. [4] G. Barles and P.L. Lions, Remarks on existence and uniqueness results for first-order Hamilton-Jacobi Equations. Proc. Coll. Franco-Esp.Pitman. Zbl0644.35015MR907716
  5. [5] G. Barles and B. Perthame, Discontinuous solutions of deterministic optimal stopping time problems. Math. Mod. Nom. Anal., t. 21, n° 4, 1987. Zbl0629.49017MR921827
  6. [6] G. Barles and B. Perthame, Exit time problems in optimal control (in preparation). 
  7. [7] E.N. Barron, Viscosity solutions for the monotone control problem. Siam J. on control and optimization. Vol. 23, n° 2, March 1985. Zbl0565.49023MR777454
  8. [8] I. Capuzzo-Dolcetta and P.L. Lions, Hamilton-Jacobi Equations and state constraints problems. To appear. MR951880
  9. [9] M.G. Crandall, L.C. Evans and P.L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi Equations. Trans. AMS, t. 282, 1984. Zbl0543.35011MR732102
  10. [10] M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton-Jacobi Equations. Trans. AMS, t. 277, 1983. Zbl0599.35024MR690039
  11. [11] M.G. Crandall, H. Ishii and P.L. Lions, Uniqueness of viscosity solutions revisited. 
  12. [12] M.G. Crandall and P.L. Lions, On existence and uniqueness of solutions of Hamilton-Jacobi Equations. Non Linear Anal. TMA. Zbl0603.35016
  13. [13] S. Delaguiche, Thèse. Université Paris IX-Dauphine. 
  14. [14] W.H. Fleming and R.W. Rishel, Deterministic and Stochastic optimal control. Springer, Berlin, 1975, Zbl0323.49001MR454768
  15. [15] H. Ishii, A simple direct proof of uniqueness for solutions of the Hamilton-Jacobi Equations of Eikonal type. Zbl0644.35017
  16. [16] H. Ishii, A boundary value problem of the Dirichlet type for Hamilton-Jacobi Equation. Zbl0701.35052MR1056130
  17. [17] H. Ishii, Perron's method for Hamilton-Jacobi Equations. Zbl0697.35030
  18. [18] H. Ishii, Remarks on the existence of viscosity solutions of Hamilton-Jacobi Equations. Bull. Facul. Sci. Eng., Chuo University, t. 26, 1983, p. 5-24. Zbl0546.35042MR742691
  19. [19] H. Ishii, Existence and Uniqueness of solutions of Hamilton-Jacobi Equations, preprint. Zbl0614.35011MR877427
  20. [20] S.N. Kruzkov, Generalized solutions of Hamilton-Jacobi Equations of Eikonal type. USSR Sbornik, t. 27, 1975, p. 406-446. Zbl0369.35012
  21. [21] J.M. Lasry and P.L. Lions, A remark on regularisation on Hilbert spaces. J. Isr. Math. Vol. 7, n° 4-1990. 
  22. [22] P.L. Lions, Generalized Solutions of Hamilton-Jacobi Equations. Pitman, London, 1982. Zbl0497.35001MR667669
  23. [23] P.L. Lions, Existence results for first-order Hamilton-Jacobi Equations. Rich. Mat. Napoli, t. 32, 1983, p. 1-23. Zbl0552.70012MR740198
  24. [24] E. Mascolo, A uniqueness result in the calculus of variations. Publi. of Universita degli studi di Salerno. Zbl0635.49003
  25. [25] E. Mascolo, Some remarks on nonconvex problems. Proc. Symposium Year on material instability in continuum mechanics, July 1986, Heriot-Watt University, Scotland. Zbl0664.49007MR970530
  26. [26] E. Mascolo, Existence results for nonconvex problems of the calculus of variations. Proc. Meet. in Calculus of Variations and P. D. E., Trento, June 1986; Springer, Lectures notes in Math. Zbl0655.49007MR974613
  27. [27] E. Mascolo and R. Schianchi, Nonconvex problems in the calculus of variations. Non Lin. Anal. TMA., vol. 9, n° 4, 1985. Zbl0545.49002MR783584
  28. [28] E. Mascolo and R. Schianchi, Existence theorems for nonconvex problems. J. Math. Pure Appl., t. 62, 1983. Zbl0522.49001MR718948
  29. [29] E. Mascolo and R. Schianchi, Un théorème d'existence pour des problèmes du calcul des variations non convexes. C. R. Acad. Sci. Paris, t. 297, série I, p. 615-617. Zbl0545.49002MR735127
  30. [30] M.H. Soner, Optimal control problems with stale space constraints. Siam J. Control Opt., May-Sept. 1986. Zbl0597.49023
  31. [31] P.E. SOUGANIDIS, Existence of viscosity solutions of Hamilton-Jacobi Equations. J. Diff. Eq. Zbl0506.35020

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.