A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations

Hitoshi Ishii

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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Ishii, 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

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  2. [2] G. Barles - B. Perthame, Personal communication. 
  3. [3] H. Brézis, Opérateur maximaux monotones et semi-groups de contraction dans les espaces de Hilbert, North-Holland, Amsterdam1973. Zbl0252.47055MR348562
  4. [4] I. Capuzzo Dolcetta - P.L. Lions, Personal communication. 
  5. [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. [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. [7] M.G. Crandall - P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc.277 (1983), 1-42. Zbl0599.35024MR690039
  8. [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. [9] H. Engler, On Hamilton-Jacobi equations in bounded domains, Proc. Royal Soc. Edinbourgh102A (1986), 221-242. Zbl0606.35014MR852356
  10. [10] H. Ishii, Representation of solutions of Hamilton-Jacobi equations, Nonlinear Anal. TMA.12 (1988), 121-146. Zbl0687.35025MR926208
  11. [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. [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. [13] H. Ishii, Perron's method for Hamilton-Jacobi equations, Duke Math. J.55 (1987), 369-384. Zbl0697.35030MR894587
  14. [14] H. Ishii - S. Koike, Remarks on elliptic singular perturbation problems, to appear in Appl. Math. Optim. Zbl0724.35009MR1076052
  15. [15] R. Jensen, New uniqueness and domain of dependence results for nonlinear first-order partial differential equations, preprint. 
  16. [16] P.L. Lions, Generalized solutions of Hamilton-Jacobi equations, Pitman, Boston, 1982. Zbl0497.35001MR667669
  17. [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. [18] P.L. Lions, Neumann type boundary conditions for Hamilton-Jacobi equations, Duke Math. J.52 (1985), 793-820. Zbl0599.35025MR816386
  19. [19] P.L. Lions, Personal communication. 
  20. [20] H.M. Soner, Optimal control with state-space constraints, I, SIAM J. Control Optim. Zbl0597.49023MR838056
  21. [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

Citations in EuDML Documents

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  1. Fabio Bagagiolo, Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities
  2. Fabio Bagagiolo, Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities
  3. Bertram Düring, Michel Fournié, Ansgar Jüngel, Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation
  4. Bertram Düring, Michel Fournié, Ansgar Jüngel, Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation
  5. Pierpaolo Soravia, Degenerate Eikonal equations with discontinuous refraction index
  6. Ariela Briani, Andrea Davini, Monge solutions for discontinuous hamiltonians
  7. Emmanuel Prados, Fabio Camilli, Olivier Faugeras, A viscosity solution method for Shape-From-Shading without image boundary data
  8. Ariela Briani, Andrea Davini, Monge solutions for discontinuous Hamiltonians

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