no. 1
A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 16 (1989) no. 1, pp. 105-135. 
@article{ASNSP_1989_4_16_1_105_0,
     author = {Ishii, Hitoshi},
     title = {A boundary value problem of the {Dirichlet} type for {Hamilton-Jacobi} equations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {105--135},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 16},
     number = {1},
     year = {1989},
     zbl = {0701.35052},
     mrnumber = {1056130},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1989_4_16_1_105_0/}
}
TY  - JOUR
AU  - Ishii, Hitoshi
TI  - A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1989
DA  - 1989///
SP  - 105
EP  - 135
VL  - Ser. 4, 16
IS  - 1
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_1989_4_16_1_105_0/
UR  - https://zbmath.org/?q=an%3A0701.35052
UR  - https://www.ams.org/mathscinet-getitem?mr=1056130
LA  - en
ID  - ASNSP_1989_4_16_1_105_0
ER  - 
%0 Journal Article
%A Ishii, Hitoshi
%T A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1989
%P 105-135
%V Ser. 4, 16
%N 1
%I Scuola normale superiore
%G en
%F ASNSP_1989_4_16_1_105_0
Ishii, Hitoshi. A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 16 (1989) no. 1, pp. 105-135. http://archive.numdam.org/item/ASNSP_1989_4_16_1_105_0/

[1] G. Barles - B. Perthame, Discontinuous solutions of deterministic optimal stopping time problems, preprint. | Numdam | MR

[2] G. Barles - B. Perthame, Personal communication.

[3] H. Brézis, Opérateur maximaux monotones et semi-groups de contraction dans les espaces de Hilbert, North-Holland, Amsterdam 1973. | MR | Zbl

[4] I. Capuzzo Dolcetta - P.L. Lions, Personal communication.

[5] M.G. Crandall - L.C. Evans - P.L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 282 (1984), 487-501. | MR | Zbl

[6] M.G. Crandall - H. Ishii - P.L. Lions, Uniqueness of viscosity solutions of Hamilton-Jacobi equations revisited, J. Math. Soc. Japan 39 (1987), 591-596. | MR | Zbl

[7] M.G. Crandall - P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-42. | MR | Zbl

[8] M.G. Crandall - R. Newcomb, Viscosity solutions of Hamilton - Jacobi equations at the boundary, Proc. Amer, Math. Soc. 94 (1985), 283-290. | MR | Zbl

[9] H. Engler, On Hamilton-Jacobi equations in bounded domains, Proc. Royal Soc. Edinbourgh 102A (1986), 221-242. | MR | Zbl

[10] H. Ishii, Representation of solutions of Hamilton-Jacobi equations, Nonlinear Anal. TMA. 12 (1988), 121-146. | MR | Zbl

[11] H. Ishii, A simple, direct proof of uniqueness for solutions of the Hamilton-Jacobi equations of eikonal type, Proc. Amer. Math. Soc. 100 (1987), 247-251. | MR | Zbl

[12] H. Ishii, Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets, Bull. Facul. Sci. & Eng. Chuo. Univ. 28 (1985), 33-77. | MR | Zbl

[13] H. Ishii, Perron's method for Hamilton-Jacobi equations, Duke Math. J. 55 (1987), 369-384. | MR | Zbl

[14] H. Ishii - S. Koike, Remarks on elliptic singular perturbation problems, to appear in Appl. Math. Optim. | MR | Zbl

[15] R. Jensen, New uniqueness and domain of dependence results for nonlinear first-order partial differential equations, preprint.

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

[17] P.L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. Part II, Comm. PDE. 8 (1983), 1229-1276. | MR | Zbl

[18] P.L. Lions, Neumann type boundary conditions for Hamilton-Jacobi equations, Duke Math. J. 52 (1985), 793-820. | MR | Zbl

[19] P.L. Lions, Personal communication.

[20] H.M. Soner, Optimal control with state-space constraints, I, SIAM J. Control Optim. | MR | Zbl

[21] P.E. Souganidis, A remark about viscosity solutions of Hamilton-Jacobi equations at the boundary, Proc. Amer. Math. Soc. 96 (1986), 323-329. | MR | Zbl