Geodesic
The vanishing viscosity method in infinite dimensions
Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 83 (1989) no. 1, pp. 79-84 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

Voir la notice de l'article

The vanishing viscosity method is adapted to the infinite dimensional case, by showing that the value function of a deterministic optimal control problem can be approximated by the solutions of suitable parabolic equations in Hilbert spaces. 
@article{RLINA_1989_8_83_1_a12,
     author = {Cannarsa, Piermarco and Da Prato, Giuseppe},
     title = {The vanishing viscosity method in infinite dimensions},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali},
     pages = {79--84},
     year = {1989},
     volume = {Ser. 8, 83},
     number = {1},
     zbl = {0735.49022},
     mrnumber = {1142442},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLINA_1989_8_83_1_a12/}
}
TY  - JOUR
AU  - Cannarsa, Piermarco
AU  - Da Prato, Giuseppe
TI  - The vanishing viscosity method in infinite dimensions
JO  - Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali
PY  - 1989
SP  - 79
EP  - 84
VL  - 83
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/RLINA_1989_8_83_1_a12/
LA  - en
ID  - RLINA_1989_8_83_1_a12
ER  - 
%0 Journal Article
%A Cannarsa, Piermarco
%A Da Prato, Giuseppe
%T The vanishing viscosity method in infinite dimensions
%J Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali
%D 1989
%P 79-84
%V 83
%N 1
%U http://geodesic.mathdoc.fr/item/RLINA_1989_8_83_1_a12/
%G en
%F RLINA_1989_8_83_1_a12
Cannarsa, Piermarco; Da Prato, Giuseppe. The vanishing viscosity method in infinite dimensions. Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 83 (1989) no. 1, pp. 79-84. http://geodesic.mathdoc.fr/item/RLINA_1989_8_83_1_a12/

[1] Barbu V. and Da Prato G., 1983. Solution of the Bellman equation associated with an infinite dimensional Stochastic control problem and synthesis of optimal control. SIAM J. Control Opt., 21, 4: 531-550. | DOI | MR | Zbl

[2] Cannarsa P. and Da Prato G. Some results on nonlinear optimal control problems and Hamilton-Jacobi equations in infinite dimensions. J. Funct. Anal., (to appear). | DOI | MR | Zbl

[3] Cannarsa P. and Da Prato G., 1989. Nonlinear optimal control with infinite horizon for distributed parameter systems and stationary Hamilton-Jacobi equations. SIAM J. Control Opt., 27, 4: 861-875. | DOI | MR | Zbl

[4] Crandall M.G. and Lions P.L., 1983. Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc., 277: 183-186. | DOI | MR | Zbl

[5] Crandall M.G. and Lions P.L., 1985. Hamilton-Jacobi equations in infinite dimensions Part I. Uniqueness of Viscosity Solutions. J. Funct. Anal., 62: 379-396. | DOI | MR | Zbl

[6] Crandall M.G. and Lions P.L., 1986. Hamilton-Jacobi equations in infinite dimensions. Part II. Existence of Viscosity Solutions. J. Funct. Anal., 65: 368-405. | DOI | MR | Zbl

[7] Crandall M.G. and Lions P.L., 1986. Hamilton-Jacobi equations in infinte dimensions. Part III. J. Funct. Anal., 68: 368-405. | DOI | MR | Zbl

[8] Crandall M.G. and Lions P.L., 1987. Solutions de visconsitê pour les équations de Hamilton-Jacobi en dimension infinie intervenant dans le contrôle optimal des problèmes d'évolution. C.R. Acad. Sci. Paris, 305: 233-236. | MR

[9] Daleckii J.L., 1966. Differential equations with functional derivatives and stochastic equations for generalized random processes. Dokl. Akad. Nauk SSSR, 166: 1035-1038. | MR

[10] Da Prato G., 1987. Some Results on Parabolic Evolution Equations with Infinitely Many Variables. J. Differential Equations, 68, 2: 281-297. | DOI | MR | Zbl

[11] Da Prato G., 1985. Some results on Bellman equation in Hilbert spaces and applications to infinite dimensional control problems. In «Stochastic Differential Systems, Filtering and Control», Lecture Notes in Control and Information Sciences n° 69, Proceedings of the IFIP-WG 7/1 Working Conference, Marseille-Luminy, France, March 12-17, 1984. MATIVIER M. and PARDOUX E. Editors: 270-280.

[12] Fleming W.H., 1969. The Cauchy problem for a nonlinear first order partial differential equation. J. Differential Equations, 5: 515-530. | DOI | MR | Zbl

[13] Gross L., 1967. Potential theory in Hilbert space. J. Func. Anal., 1: 123-181. | MR | Zbl

[14] Havarneanu T., 1985. Existence for the Dynamic Programming equations of control diffusion processes in Hilbert spaces. Nonlinear Anal. T.M.A, 9, n° 6: 619-629. | DOI | MR | Zbl

[15] Lions P.L., 1982. Generalized solutions of Hamilton-Jacobi equations. Pitman, Boston. | Zbl

[16] Piech M.A., 1969. A Fundamental Solution of the Parabolic Equations in Hilbert spaces. J. Funct. Analysis, 3: 85-114. | MR | Zbl