@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}, pages = {237--269}, publisher = {Elsevier}, volume = {20}, number = {2}, year = {2003}, doi = {10.1016/S0294-1449(02)00010-0}, zbl = {1029.35067}, language = {en}, url = {http://www.numdam.org/articles/10.1016/S0294-1449(02)00010-0/} }
TY - JOUR AU - Siconolfi, Antonio TI - Almost continuous solutions of geometric Hamilton-Jacobi equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2003 SP - 237 EP - 269 VL - 20 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S0294-1449(02)00010-0/ DO - 10.1016/S0294-1449(02)00010-0 LA - en ID - AIHPC_2003__20_2_237_0 ER -
%0 Journal Article %A Siconolfi, Antonio %T Almost continuous solutions of geometric Hamilton-Jacobi equations %J Annales de l'I.H.P. Analyse non linéaire %D 2003 %P 237-269 %V 20 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/S0294-1449(02)00010-0/ %R 10.1016/S0294-1449(02)00010-0 %G en %F 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) no. 2, pp. 237-269. doi : 10.1016/S0294-1449(02)00010-0. http://www.numdam.org/articles/10.1016/S0294-1449(02)00010-0/
[1] Optimal Control and Viscosity Solutions of Hamilton-Jacobi Equations, Birkhäuser, Boston, 1997. | MR | Zbl
, ,[2] Viscosity Solutions and Applications, Springer-Verlag, Berlin, 1997.
, , , ,[3] Exit time problems in optimal control and vanishing viscosity method, SIAM J. Control Optim. 26 (1988) 1133-1148. | MR | Zbl
, ,[4] Discontinuous viscosity solutions of first order of Hamilton-Jacobi equations: a guided visit, Nonlinear Anal. 20 (1993) 1123-1134. | MR | Zbl
,[5] Solutions de Viscosité des Équations de Hamilton-Jacobi, Springer-Verlag, Paris, 1994. | MR | Zbl
,[6] Semicontinuous viscosity solutions of Hamilton-Jacobi equations with convex Hamiltonians, Comm. Partial Differential Equations 15 (1990) 1713-1742. | MR | Zbl
, ,[7] Uniqueness and existence of viscosity solutions of generalized mean curvature flow equation, J. Differential Geom. 33 (1991) 749-786. | MR | Zbl
, , ,[8] Optimization and Nonsmooth Analysis, Wiley, New York, 1983. | MR | Zbl
,[9] Differential games and nonlinear first order PDE in bounded domains, Manuscripta Math. 49 (1984) 109-139. | MR | Zbl
, ,[10] Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations, Indiana Univ. Math. J. 33 (1984) 773-797. | MR | Zbl
, ,[11] Lower semicontinuous solutions of Hamilton-Jacob-Bellman equations, SIAM J. Control. Optim. 31 (1993) 257-272. | MR | Zbl
,[12] Y. Giga, M.H. Sato, A level set approach to semicontinuous viscosity solutions for Cauchy problems, Preprint, 1999. | MR
[13] Perron's method for Hamilton-Jacobi equations, Duke Math. J. 55 (1987) 369-384. | MR | Zbl
,[14] General Topology, Van Nostrand, Princeton, 1955. | MR | Zbl
,[15] Measure and Category, Springer-Verlag, New York, 1971. | MR | Zbl
,[16] Generalized directional derivatives and subgradients of nonconvex functions, Can. J. Math. 32 (1980) 257-280. | MR | Zbl
,[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 | Zbl
[19] A. Siconolfi, Representation formulae and comparison results for geometric Hamilton-Jacobi equations, Preprint, 2001.
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