A density approach to Hamilton-Jacobi equations with t-measurable Hamiltonians

Nonlinear Differential Equations and Applications

Volumn 12, Issue 1, 2005, Pages 71-91

  Briani, Ariela ^a   Rampazzo, Franco ^b  

^a UNIVERSITY OF PISA   (Italy)

^b UNIVERSITY OF PADOVA   (Italy)

Author keywords

Hamilton Jacobi equations; Viscosity solutions

Indexed keywords

EID: 21644448842     PISSN: 10219722     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00030-004-2030-4     Document Type: Article

References (12)

1. [Ba94] G. BARLES, Solutions de viscositè des equations de Hamilton-Jacobi, Springer-Verlag, Berlin 1994.
2. [BCD97] M. BABDI, I. CAPUZZO DOLCETTA, Optimal control and viscosity solution of Hamilton-Jacobi-Bellman equations, Birkäuser, Boston 1997.
3. [BJ87] E.N. BARRON, R. JENSEN, Generalized viscosity solution for Hamilton-Jacobi equations with time-measurable Hamiltonians, J. Differential Equations 68 (1987), 10-21.
4. [CP00] P. CARDALIAGUET, S. PLASKACZ, Invariant solutions of differential games and Hamilton-Jacobi equations for time-measurable Hamiltonians, SIAM J. Control Optim. 38 (2000), 1501-1520.
5. [CL87] M. CRANDALL, P.L. LIONS, Remarks on the existence and uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations, Illinois Journal of Mathematics 31 (1987), 665-688.
6. [Is84] H. ISHII, Uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations, Indiana Univ. Math. J. 33 (1984), 721-748.
7. [Is85] H. ISHII, Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets, Bull. Facul. Sci. & Eng. 28 (1985), 33-77.
8. [Is87] H. ISHII, A comparison result for Hamilton-Jacobi equations without growth condition on solutions from above, Appl. Anal. 67 (1987), 357-372.
9. [Le01] O. LEY, Lower bound gradient estimate for first-order Hamilton-Jacobi equations and applications to the regularity of propagations fronts, Adv. Differential Equations 6(5) (2001), 547-576.
10. [LP87] P.L. LIONS, B. PERTHAME, Remarks on Hamilton-Jacobi equations with measurable time-dependent Hamiltonians, Nonlinear analysis, Theory, Methods & Applications 11(5) (1987), 613-612.
11. [Nu90] D. NUNZIANTE, Uniqueness of viscosity solutions of fully nonlinear second order parabolic equations with discontinuous time dependence, Differential Integral Equations 3(1) (1990), 77-91.
12. [Nu92] D. NUNZIANTE, Existence and uniqueness of unbounded viscosity solutions of parabolic equations with discontinuous time-dependence, Nonlinear Anal. 18(11) (1992), 1033-1062.