Metric character of Hamilton-Jacobi equations

Transactions of the American Mathematical Society

Volumn 355, Issue 5, 2003, Pages 1987-2009

  Siconolfi, Antonio ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Distance functions; Hamilton Jacobi equations; Viscosity solutions

Indexed keywords

EID: 0037407041     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-03-03237-9     Document Type: Article

References (15)

1. M. Bardi and I. Capuzzo Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Birkhäuser, Boston, 1997. MR 99e:49001
2. M. Bardi and L. C. Evans, "On Hopf's formulas for solutions of Hamilton-Jacobi equations", Nonlinear Anal. TMA 8 (1984), 1373-1381. MR 85k:35043
3. G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi, Springer, Paris, 1994. MR 2000b:49054
4. L. M. Blumenthal, Theory and applications of distance geometry, Oxford Univ. Press, London, 1953, reprinted Chelsea Publ., New York, 1979. MR 14:1009a; MR 42:3678
5. H. Busemann, Metric methods in Finsler spaces and in the foundations of geometry, Ann. Math. Study, Princeton, 1942. MR 4:109e
6. H. Busemann, The geometry of geodesics, Academic Press, New York, 1955. MR 17:779a
7. H. Busemann and W. Mayer, "On the foundations of calculus of variations", Trans. Amer. Math. Soc. 49 (1941), 173-198. MR 2:225d
8. F. Camilli and A. Siconolfi, "Maximal subsolutions for a class of degenerate Hamilton-Jacobi equations", Indiana Univ. Math. J. 48 (1999), 1111-1131. MR 2001a:49028
9. F. Camilli and A. Siconolfi, "Nonconvex degenerate Hamilton-Jacobi equations", Math. Z, 242 (2002), 1-21.
10. R. Courant and D. Hubert, Methods of Mathematical Physics, Volume II, John Wiley, New York, 1962, reprinted 1989. MR 25:4216; MR 90k:35001
11. L. C. Evans and H. Ishii, "Differential games and nonlinear first order PDE in bounded domains", Manuscripta Math. 49 (1984), 109-139. MR 86f:35048
12. L. C. Evans and P. Souganidis, "Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations", Indiana Univ. Math. J. 33 (1984), 773-797. MR 86d:90185
13. S. N. Kruzkov, "Generalized solutions of the Hamilton-Jacobi equations of eikonal type", Math. USSR Sbornik 27 (1975), 406-446. MR 53:8670
14. M. Gromov, Metric structures for Riemannian and non-Riemannian spaces, Birkhäuser, Boston, 1998. MR 2000d:53065
15. P. L. Lions, Generalized solutions of Hamilton-Jacobi equations, Pitman, London, 1982. MR 84a:49038