A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1989)
- Volume: 16, Issue: 1, page 105-135
- ISSN: 0391-173X
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topIshii, Hitoshi. "A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 16.1 (1989): 105-135. <http://eudml.org/doc/84047>.
@article{Ishii1989,
author = {Ishii, Hitoshi},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Dirichlet boundary conditions; Hamilton-Jacobi equation; viscosity solution; optimal control theory},
language = {eng},
number = {1},
pages = {105-135},
publisher = {Scuola normale superiore},
title = {A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations},
url = {http://eudml.org/doc/84047},
volume = {16},
year = {1989},
}
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
PB - Scuola normale superiore
VL - 16
IS - 1
SP - 105
EP - 135
LA - eng
KW - Dirichlet boundary conditions; Hamilton-Jacobi equation; viscosity solution; optimal control theory
UR - http://eudml.org/doc/84047
ER -
References
top- [1] G. Barles - B. Perthame, Discontinuous solutions of deterministic optimal stopping time problems, preprint. MR921827
- [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, Amsterdam1973. Zbl0252.47055MR348562
- [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. Zbl0543.35011MR732102
- [6] M.G. Crandall - H. Ishii - P.L. Lions, Uniqueness of viscosity solutions of Hamilton-Jacobi equations revisited, J. Math. Soc. Japan39 (1987), 591-596. Zbl0644.35016MR905626
- [7] M.G. Crandall - P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc.277 (1983), 1-42. Zbl0599.35024MR690039
- [8] M.G. Crandall - R. Newcomb, Viscosity solutions of Hamilton - Jacobi equations at the boundary, Proc. Amer, Math. Soc.94 (1985), 283-290. Zbl0575.35008MR784180
- [9] H. Engler, On Hamilton-Jacobi equations in bounded domains, Proc. Royal Soc. Edinbourgh102A (1986), 221-242. Zbl0606.35014MR852356
- [10] H. Ishii, Representation of solutions of Hamilton-Jacobi equations, Nonlinear Anal. TMA.12 (1988), 121-146. Zbl0687.35025MR926208
- [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. Zbl0644.35017MR884461
- [12] H. Ishii, Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets, Bull. Facul. Sci. & Eng. Chuo. Univ.28 (1985), 33-77. Zbl0937.35505MR845397
- [13] H. Ishii, Perron's method for Hamilton-Jacobi equations, Duke Math. J.55 (1987), 369-384. Zbl0697.35030MR894587
- [14] H. Ishii - S. Koike, Remarks on elliptic singular perturbation problems, to appear in Appl. Math. Optim. Zbl0724.35009MR1076052
- [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. Zbl0497.35001MR667669
- [17] P.L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. Part II, Comm. PDE. 8 (1983), 1229-1276. Zbl0716.49023MR709162
- [18] P.L. Lions, Neumann type boundary conditions for Hamilton-Jacobi equations, Duke Math. J.52 (1985), 793-820. Zbl0599.35025MR816386
- [19] P.L. Lions, Personal communication.
- [20] H.M. Soner, Optimal control with state-space constraints, I, SIAM J. Control Optim. Zbl0597.49023MR838056
- [21] P.E. Souganidis, A remark about viscosity solutions of Hamilton-Jacobi equations at the boundary, Proc. Amer. Math. Soc.96 (1986), 323-329. Zbl0598.35066MR818466
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- Pierpaolo Soravia, Degenerate Eikonal equations with discontinuous refraction index
- Bertram Düring, Michel Fournié, Ansgar Jüngel, Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation
- Ariela Briani, Andrea Davini, Monge solutions for discontinuous hamiltonians
- Ariela Briani, Andrea Davini, Monge solutions for discontinuous Hamiltonians
- Emmanuel Prados, Fabio Camilli, Olivier Faugeras, A viscosity solution method for Shape-From-Shading without image boundary data
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