Almost continuous solutions of geometric Hamilton–Jacobi equations

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1. [1] Bardi M., Capuzzo Dolcetta I., Optimal Control and Viscosity Solutions of Hamilton–Jacobi Equations, Birkhäuser, Boston, 1997. Zbl0890.49011MR1484411
2. [2] Bardi M., Crandall M.G., Evans L.C., Souganidis P.E., Viscosity Solutions and Applications, Springer-Verlag, Berlin, 1997. 
3. [3] Barles G., Perthame B., Exit time problems in optimal control and vanishing viscosity method, SIAM J. Control Optim.26 (1988) 1133-1148. Zbl0674.49027MR957658
4. [4] Barles G., Discontinuous viscosity solutions of first order of Hamilton–Jacobi equations: a guided visit, Nonlinear Anal.20 (1993) 1123-1134. Zbl0816.35081MR1216503
5. [5] Barles G., Solutions de Viscosité des Équations de Hamilton–Jacobi, Springer-Verlag, Paris, 1994. Zbl0819.35002MR1613876
6. [6] Barron E.N., Jensen R., Semicontinuous viscosity solutions of Hamilton–Jacobi equations with convex Hamiltonians, Comm. Partial Differential Equations15 (1990) 1713-1742. Zbl0732.35014MR1080619
7. [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. Zbl0696.35087MR1100211
8. [8] Clarke F.H., Optimization and Nonsmooth Analysis, Wiley, New York, 1983. Zbl0582.49001MR709590
9. [9] Evans L.C., Ishii H., Differential games and nonlinear first order PDE in bounded domains, Manuscripta Math.49 (1984) 109-139. Zbl0559.35013MR767202
10. [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. Zbl1169.91317MR756158
11. [11] Frankowska H., Lower semicontinuous solutions of Hamilton–Jacob–Bellman equations, SIAM J. Control. Optim.31 (1993) 257-272. Zbl0796.49024MR1200233
12. [12] Y. Giga, M.H. Sato, A level set approach to semicontinuous viscosity solutions for Cauchy problems, Preprint, 1999. Zbl1005.49025MR1843285
13. [13] Ishii H., Perron's method for Hamilton–Jacobi equations, Duke Math. J.55 (1987) 369-384. Zbl0697.35030MR894587
14. [14] Kelley J.L., General Topology, Van Nostrand, Princeton, 1955. Zbl0066.16604MR70144
15. [15] Oxtoby J.C., Measure and Category, Springer-Verlag, New York, 1971. Zbl0217.09201MR584443
16. [16] Rockafellar R.T., Generalized directional derivatives and subgradients of nonconvex functions, Can. J. Math.32 (1980) 257-280. Zbl0447.49009MR571922
17. [17] S. Samborski, Extension of nonlinear partial differential expressions and viscosity solutions. An useful space, Preprint, 2000. 
18. [18] A. Siconolfi, Metric character of Hamilton–Jacobi equations, Trans. Amer. Math. Soc., to appear. Zbl1026.35027MR1953535
19. [19] A. Siconolfi, Representation formulae and comparison results for geometric Hamilton–Jacobi equations, Preprint, 2001.