Nonsmooth multi-time Hamilton-Jacobi systems

Indiana University Mathematics Journal

Volumn 55, Issue 5, 2006, Pages 1573-1614

  Motta, Monica ^a   Rampazzo, Franco ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

Commutativity of minimum problems; Lie brackets; Systems of HJ equations

Indexed keywords

EID: 33845528580     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2006.55.2760     Document Type: Article

References (22)

1. ANDREI A. AGRACHEV and REVAZ V. GAMKRELIDZE, Exponential representation of flows and a chronological enumeration, Mat. Sb. (N.S.) 107(149) (1978), 467-532, 639. MR 524203 (80g:49036) (Russian)
2. GUY BARLES and BENOÎT PERTHAME, Exit time problems in optimal control and vanishing viscosity method, SIAM J. Control Optim. 26 (1988), 1133-1148, http://dx.doi.org/10-1137/0326063. MR 957658 (891:49021) (English, with French summary)
3. GUY BARLES and AGNÈS TOURIN, Commutation properties of semigroups for first-order Hamilton-Jacobi equations and application to multi-time equations, Indiana Univ. Math. J. 50 (2001), 1523-1544, http://dx.doi.org/10. 1512/iumj.2001.50.1925. MR 1889069 (2003a:49037)
4. MARTINO BARDI and ITALO CAPUZZO-DOLCETTA, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Systems & Control: Foundations & Applications, Birkhauser Boston Inc., Boston, MA, 1997, ISBN 0-8176-3640-4. MR 1484411 (99e:49001)
5. ARIELA BRIANI and FRANCO RAMPAZZO, A density approach to Hamilton-Jacobi equations with t-measurable Hamiltonians, NoDEA Nonlinear Differential Equations Appl. 12 (2005), 71-91, http://dx.doi.org/10.1007/s00030-004-2030-4. MR 2138935 (2006b:49062)
6. YUN GANG CHEN, YOSHIKAZU GIGA, and SHUN'ICHI GOTO, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Differential Geom. 33 (1991), 749-786, http://dx.doi.org/10.1016/0022- 0396(91)90116-Q. MR 1100211 (93a:35093)
7. MICHAEL G. CRANDALL, LAWRENCE C. EVANS, and PIERRE-LOUIS LIONS, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 282 (1984), 487-502, http://dx.doi.org/10.2307/1999247. MR 732102 (86a:35031)
8. MICHAEL G. CRANDALL and RICHARD NEWCOMB, Viscosity solutions of Hamilton-Jacobi equations at the boundary, Proc. Amer. Math. Soc. 94 (1985), 283-290, http://dx.doi.org/10.2307/2045392. MR 784180 (86f:35047)
9. LAWRENCE C. EVANS and PANAGIOTIS E. SOUGANIDIS, Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations, Indiana Univ. Math. J. 33 (1984), 773-797, http://dx.doi.org/10.1512/iumj.1984. 33.33040. MR 756158 (86d:90185)
10. LAWRENCE C. EVANS and J. SPRUCK, Motion of level sets by mean curvature. 1, J. Differential Geom. 33 (1991), 635-681. MR 1100206 (92h:35097)
11. HITOSHI ISHII, Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets, Bull. Fac. Sci. Engrg. Chuo Univ. 28 (1985), 33-77. MR 845397 (87k:35055)
12. -, A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16 (1989), 105-135. MR 1056130 (91f:35071)
13. -, On representations of solutions of Hamilton-Jacobi equations with convex Hamiltonians (K. Masuda and M. Mimura, eds.), Proc. Recent Topics in Nonlinear PDE, II, Sendai, 1984, North-Holland Math. Stud., vol. 128, North-Holland, Amsterdam, 1985, pp. 15-52. MR 882926 (88i:35024)
14. PIERRE-LOUIS LIONS and BENOIT PERTHAME, Remarks on Hamilton-Jacobi equations with measurable time-dependent Hamiltonians, Nonlinear Anal. 11 (1987), 613-621, http://dx.doi.org/10.1016/0362-546X(87)90076-9. MR 886652 (88e:49057)
15. PIERRE-LOUIS LIONS and JEAN-CHARLES ROCHET, Hopf formula and multitime Hamilton-Jacobi equations, Proc. Amer. Math. Soc. 96 (1986), 79-84, http://dx.doi.org/10.2307/2045657. MR 813815 (87h:35056)
16. PETER J. OLVER, Equivalence, Invariants, and Symmetry, Cambridge University Press, Cambridge, 1995, ISBN 0-521-47811-1. MR 1337276 (96i:58005)
17. SŁAWOMIR PLASKACZ and MARC QUINCAMPOIX, On representation formulas for Hamilton Jacobi's equations related to calculus of variations problems, Topol. Methods Nonlinear Anal. 20 (2002), 85-118. MR 1940532 (2003k:49060)
18. FRANCO RAMPAZZO, Faithful representations for convex Hamilton-Jacobi equations, SIAM J. Control Optim. 44 (2005), 867-884 (electronic), http://dx.doi.org/10.1137/S0363012903436855. MR 2178049 (2006h:49010)
19. -, Flows' commutativity of control vector fields and inf-commutativity, Dipartimento di Matematica Pura e Applicata dell' Università di Padova, 2004 (preprint).
20. FRANCO RAMPAZZO and HÉCTOR SUSSMANN J., Set-valued differentials and a nonsmooth version of Chow's theorem, Proc. The 40th IEEE Conference on Decision and Control; Orlando, Florida, December 4 to 7, 2001, IEEE Publications, vol. 3, New York, 2001, pp. 2613-2618.
21. -, Commutators of nonsmooth vector fields, J. Differential Equations (to appear).
22. JEAN-CHARLES ROCHET, The taxation principle and multitime Hamilton-Jacobi equations, J. Math. Econom. 14 (1985), 113-128, http://dx.doi.org/10.1016/0304- 4068(85)90015-1. MR 827147 (87g:90039)