# Discontinuous solutions of deterministic optimal stopping time problems

- Volume: 21, Issue: 4, page 557-579
- ISSN: 0764-583X

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topBarles, G., and Perthame, B.. "Discontinuous solutions of deterministic optimal stopping time problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 21.4 (1987): 557-579. <http://eudml.org/doc/193514>.

@article{Barles1987,

author = {Barles, G., Perthame, B.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {discontinuous obstacle; deterministic optimal stopping time problem; viscosity solution; Bellman variational inequality; minimum exit time from a domain},

language = {eng},

number = {4},

pages = {557-579},

publisher = {Dunod},

title = {Discontinuous solutions of deterministic optimal stopping time problems},

url = {http://eudml.org/doc/193514},

volume = {21},

year = {1987},

}

TY - JOUR

AU - Barles, G.

AU - Perthame, B.

TI - Discontinuous solutions of deterministic optimal stopping time problems

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 1987

PB - Dunod

VL - 21

IS - 4

SP - 557

EP - 579

LA - eng

KW - discontinuous obstacle; deterministic optimal stopping time problem; viscosity solution; Bellman variational inequality; minimum exit time from a domain

UR - http://eudml.org/doc/193514

ER -

## References

top- [1] I. CAPUZZO-DOLCETTA and H. ISHII, Approximate solutions of the Bellman Equations of deterministic control theory. Applied Math, andOpt. 11, (1984),pp. 161-181. Zbl0553.49024MR743925
- [2] I. CAPUZZO-DOLCETTA and P. L. LIONS, Hamilton-JacobiEquations and state- constraints problems ; In preparation. Zbl0702.49019
- [3] M. G. CRANDALL, L. C. EVANS and P. L. LIONS, Some properties of viscosity solutions of Hamilton-Jacobi Equations ; Trans. Amer. Math. Soc., 282 (1984). Zbl0543.35011MR732102
- [4] M. G. CRANDALL, H. ISHII, and P. L. LIONS, Uniqueness of viscosity solutions revisited ; to appear. Zbl0644.35016
- [5] M. G. CRANDALL and P. L. LIONS, Viscosity solutions of Hamilton-Jacobi Equations ; Trans. Amer. Math. Soc., 277 (1983). Zbl0599.35024MR690039
- [6] M. G. CRANDALL and P. L. LIONS, On existence and uniqueness of solutions of Hamilton-Jacobi Equations ; Non Linear Anal. TMA. Vol. 10, N°6 (1986). Zbl0603.35016MR836671
- [7] W. H. FLEMING and R. W. RISHEL, Deterministic and stochastic optimal control. Springer, Berlin 1975. Zbl0323.49001MR454768
- [8] H. ISHII, Hamilton-Jacobi Equations with discontinuous Hamiltonians on arbitrary open subsets. Zbl0937.35505
- [9] H. ISHII, Perron's method for Hamilton-Jacobi Equations ; to appear. Zbl0697.35030
- [10] E. B. LEE and L. MARKUS, Foundations of optimal control theory, J. Wiley, New York (1967). Zbl0159.13201MR220537
- [11] P. L. LIONS, Generalized solutions of Hamilton-Jacobi Equations. Pitman, 1982. Zbl0497.35001MR667669
- [12] P. L. LIONS and B. PERTHAME, Remarks on Hamilton-Jacobi Equations with discontinuous time-dependent coefficients ; Non Linear Anal. TMA. Vol. 11, n° 7 (1987). Zbl0688.35052MR886652
- [13] P. L. LIONS and P. E. SOUGANIDIS, Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaac's Equations ; SIAM J. Control and Optimization, vol. 23, n° 4 (1985). Zbl0569.49019MR791888
- [14] J. P. QUADRAT, in Thèse d'Etat, Univ. Paris IX-Dauphine. Zbl0546.22019
- [15] M. H. SONER, Optimal controlproblems with state-space constraints. SIAM J.on Control and Optimisation. Vol. 24, n° 3, pp. 551-561 and Vol. 24, n° 4, pp. 1110-1122. Zbl0619.49013MR861089
- [16] J. WARGA, Optimal control of differential and functionnal equations. Academic press, (1972). Zbl0253.49001MR372708

## Citations in EuDML Documents

top- Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani, Deterministic state-constrained optimal control problems without controllability assumptions
- Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani, Deterministic state-constrained optimal control problems without controllability assumptions
- I. Capuzzo Dolcetta, M. Falcone, Discrete dynamic programming and viscosity solutions of the Bellman equation
- Bertram Düring, Michel Fournié, Ansgar Jüngel, Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation
- Pierpaolo Soravia, Degenerate Eikonal equations with discontinuous refraction index
- Magdalena Kobylanski, Large deviations principle by viscosity solutions: the case of diffusions with oblique Lipschitz reflections
- G. Barles, An approach of deterministic control problems with unbounded data
- Bertram Düring, Michel Fournié, Ansgar Jüngel, Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation
- Italo Capuzzo Dolcetta, Soluzioni di viscosità

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