Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
G. Barles: Existence results for first order Hamilton-Jacobi equations. To appear in Ann. I.H.P. Anal. Non Lin., see also Thèse de 3e. cycle, Paris-Dauphine, 1983.
G. Barles: Some remarks on existence results for first-order Hamilton-Jacobi equations, Submitted to Ann. I.H.P. Anal. Non Lin.
G. Barles: Quasi-variational inequalities and first-order Hamilton-Jacobi equations. Thèse de 3e. cycle. Paris-Dauphine, 1983.
G. Barles: Determinisitc impulsive control problems. To appear in SIAM J. Control. Optim., see also Thèse de 3e. cycle, Paris-Dauphine, 1983.
I. Capuzzo-Dolcetta: On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming. Appl. Math. Optim. 10 (1983), p. 367–377.
I. Capuzzo-Dolcetta and L.C. Evans: Optimal switching for ordinary differential equations. SIAM J. Control Optim., 22 (1984) p. 143–46.
M.G. Crandall, L.C. Evans and P.L. Lions: Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc., 1984.
M.G. Crandall and P.L. Lions: Conditions d’unicité pour les solutions généralisées des equations de Hamilton-Jacobi du premier ordre. C.R. Acad. Sci. Paris, 292 (1981), p. 183–186.
M.G. Crandall and P.L. Lions: Viscosity solutions of Hamilton-Jacobi equations. Trans Amer. Math. Soc., 277 (1983), p. 1–42.
M.G. Crandall and P.L. Lions: Solutions de viscosité non barnées des equations de Hamilton-Jacobi du premier ordre. C.R. Acad. Sci. Paris, 1984.
L.C. Evans and H. Ishii: Differential games and nonlinear first order PDE on bounded domains, to appear.
L.C. Evans and H. Ishii: A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities, to appear.
W.H. Fleming and R. Rishel: Deterministic and stochastic optimal control. Springer, Berlin, 1975.
W.H. Fleming and P.E. Souganidis: to appear.
H. Ishii: Uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations. To appear in Ind. Univ. Math. J.
P.L. Lions: Generalized solutions of Hamilton-Jacobi equations. Pitman, London, 1982.
P.L. Lions: Existence results for first-order Hamilton-Jacobi equations. Ricerche di Mat., 32 (1983), p. 3–23
P.L. Lions: Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. Parts 1,2. Comm. P.D.E., 8 (1983), p. 1101–1174, p. 1229–1276.
P.L. Lions: Some recent results in the optimal control of diffusion processes. Stochastic Analysis, Proceedings of the Taniguchi International Symposium on Stochastic Analysis, Katata and Kyoto, 1982. Kinokuniya, Tokyo, 1984.
P.L. Lions: On the Hamilton-Jacobi-Bellman equations. Acta Applicanda, 1 (1983), p. 17–41.
P.L. Lions: Fully nonlinear elliptic equations and applications. In Nonlinear Analysis, Function Spaces and Applications, Teubner, Leipzig, 1982.
P.L. Lions and M. Nisio: A uniqueness result for the semigroup associated with the Hamilton-Jacobi-Bellman operator. Proc. Japan Acad., 58 (1982), p. 273–276.
P.L. Lions and P.E. Souganidis: Differential games, optimal control and directional derivatives of viscosity solutions of Bellman’s and Isaacs’ equations. To appear in SIAM J. Control Optim.
P.E. Souganidis: PhD Thesis, University of Wisconsin-Madison, 1983.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag
About this paper
Cite this paper
Lions, P.L. (1985). Optimal control and viscosity solutions. In: Dolcetta, I.C., Fleming, W.H., Zolezzi, T. (eds) Recent Mathematical Methods in Dynamic Programming. Lecture Notes in Mathematics, vol 1119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074782
Download citation
DOI: https://doi.org/10.1007/BFb0074782
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15217-0
Online ISBN: 978-3-540-39365-8
eBook Packages: Springer Book Archive