Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Hopf formula and multitime Hamilton-Jacobi equations


Authors: P.-L. Lions and J.-C. Rochet
Journal: Proc. Amer. Math. Soc. 96 (1986), 79-84
MSC: Primary 35F99; Secondary 35L40, 90A16
DOI: https://doi.org/10.1090/S0002-9939-1986-0813815-5
MathSciNet review: 813815
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Problems arising in mathematical economics lead to the study of multi-time Hamilton-Jacobi equations. Using commutation properties of the semigroups for the standard equation, we propose a generalization of the Hopf formula that gives explicit solutions of these equations.


References [Enhancements On Off] (What's this?)

  • [1] M. Bardi and L. C Evans, On Hopf's formulas for solutions of Hamilton-Jacobi equations, preprint.
  • [2] M. G. Crandall and P. L. Lions, Conditions d'unicité pour les solutions généralisées des équations de Hamilton-Jacobi du premier ordre, C. R. Acad. Sci. Paris 292 (1981), 183-186. MR 610314 (82c:49020)
  • [3] -, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-42. MR 690039 (85g:35029)
  • [4] -, Solutions de viscosité non bornées des équations de Hamilton-Jacobi du premier ordre, C. R. Acad. Sci. Paris (in preparation).
  • [5] E. Hopf, Generalized solutions of nonlinear equations of first order, J. Math. Mech. 14 (1965), 951-973. MR 0182790 (32:272)
  • [6] H. Ishii, Uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations, preprint. MR 756156 (85h:35057)
  • [7] P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math. 10 (1957), 537-566. MR 0093653 (20:176)
  • [8] P. L. Lions, Generalized solutions of Hamilton-Jacobi equations, Pitman, London, 1982. MR 667669 (84a:49038)
  • [9] P. L. Lions and M. Nisio, A uniqueness result for the semigroup associated with the Hamilton Jacobi Bellman operation, Proc. Japan Acad. Math. Sci. 58 (1982), 273-276. MR 682680 (84b:49032)
  • [10] J. C. Rochet, The taxation principle and multi-time Hamilton-Jacobi equations, preprint, Univ. Paris IX.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35F99, 35L40, 90A16

Retrieve articles in all journals with MSC: 35F99, 35L40, 90A16


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0813815-5
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society