Almost continuous solutions of geometric Hamilton-Jacobi equations
Siconolfi, Antonio
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003), p. 237-269 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2003__20_2_237_0,
     author = {Siconolfi, Antonio},
     title = {Almost continuous solutions of geometric Hamilton-Jacobi equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {20},
     year = {2003},
     pages = {237-269},
     doi = {10.1016/S0294-1449(02)00010-0},
     zbl = {1029.35067},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2003__20_2_237_0}
}

Siconolfi, Antonio. Almost continuous solutions of geometric Hamilton-Jacobi equations. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) pp. 237-269. doi : 10.1016/S0294-1449(02)00010-0. http://gdmltest.u-ga.fr/item/AIHPC_2003__20_2_237_0/

[1] Bardi M., Capuzzo Dolcetta I., Optimal Control and Viscosity Solutions of Hamilton-Jacobi Equations, Birkhäuser, Boston, 1997. | MR 1484411 | Zbl 0890.49011

[2] Bardi M., Crandall M.G., Evans L.C., Souganidis P.E., Viscosity Solutions and Applications, Springer-Verlag, Berlin, 1997.

[3] Barles G., Perthame B., Exit time problems in optimal control and vanishing viscosity method, SIAM J. Control Optim. 26 (1988) 1133-1148. | MR 957658 | Zbl 0674.49027

[4] Barles G., Discontinuous viscosity solutions of first order of Hamilton-Jacobi equations: a guided visit, Nonlinear Anal. 20 (1993) 1123-1134. | MR 1216503 | Zbl 0816.35081

[5] Barles G., Solutions de Viscosité des Équations de Hamilton-Jacobi, Springer-Verlag, Paris, 1994. | MR 1613876 | Zbl 0819.35002

[6] Barron E.N., Jensen R., Semicontinuous viscosity solutions of Hamilton-Jacobi equations with convex Hamiltonians, Comm. Partial Differential Equations 15 (1990) 1713-1742. | MR 1080619 | Zbl 0732.35014

[7] Chen Y.G., Giga Y., Goto S., Uniqueness and existence of viscosity solutions of generalized mean curvature flow equation, J. Differential Geom. 33 (1991) 749-786. | MR 1100211 | Zbl 0696.35087

[8] Clarke F.H., Optimization and Nonsmooth Analysis, Wiley, New York, 1983. | MR 709590 | Zbl 0582.49001

[9] Evans L.C., Ishii H., Differential games and nonlinear first order PDE in bounded domains, Manuscripta Math. 49 (1984) 109-139. | MR 767202 | Zbl 0559.35013

[10] Evans L.C., Souganidis P., Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations, Indiana Univ. Math. J. 33 (1984) 773-797. | MR 756158 | Zbl 1169.91317

[11] Frankowska H., Lower semicontinuous solutions of Hamilton-Jacob-Bellman equations, SIAM J. Control. Optim. 31 (1993) 257-272. | MR 1200233 | Zbl 0796.49024

[12] Y. Giga, M.H. Sato, A level set approach to semicontinuous viscosity solutions for Cauchy problems, Preprint, 1999. | MR 1843285

[13] Ishii H., Perron's method for Hamilton-Jacobi equations, Duke Math. J. 55 (1987) 369-384. | MR 894587 | Zbl 0697.35030

[14] Kelley J.L., General Topology, Van Nostrand, Princeton, 1955. | MR 70144 | Zbl 0066.16604

[15] Oxtoby J.C., Measure and Category, Springer-Verlag, New York, 1971. | MR 584443 | Zbl 0217.09201

[16] Rockafellar R.T., Generalized directional derivatives and subgradients of nonconvex functions, Can. J. Math. 32 (1980) 257-280. | MR 571922 | Zbl 0447.49009

[17] S. Samborski, Extension of nonlinear partial differential expressions and viscosity solutions. An useful space, Preprint, 2000.

[18] A. Siconolfi, Metric character of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., to appear. | MR 1953535 | Zbl 1026.35027

[19] A. Siconolfi, Representation formulae and comparison results for geometric Hamilton-Jacobi equations, Preprint, 2001.