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Discontinuous viscosity solutions of first-order Hamilton-Jacobi equations: A guided visit. (English) Zbl 0816.35081
The author presents some recent developments in the theory of discontinuous viscosity solutions of first-order Hamilton-Jacobi equations where he is one of the main contributors.

MSC:
35L60 First-order nonlinear hyperbolic equations
70H20 Hamilton-Jacobi equations in mechanics
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[1] Barron, E.N.; Jensen, R., Semicontinuous viscosity solutions of Hamilton-Jacobi. equations with convex Hamiltonians, Communs partial diff. eqns, 15, 1713-1742, (1990) · Zbl 0732.35014
[2] Barron, E.N.; Jensen, R., Optimal control and semicontinuous viscosity solutions, Proc. am. math. soc., 113, 397-402, (1991) · Zbl 0741.49010
[3] Crandall, M.G.; Lions, P.L., Viscosity solutions of Hamilton-Jacobi, Trans. am. math. soc., 277, (1983) · Zbl 0874.49025
[4] Crandall, M.G.; Evans, L.C.; Lions, P.L., Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. am. math. soc., 282, 1-42, (1984) · Zbl 0543.35011
[5] Lions, P.L., Generalized solutions of Hamilton-Jacobi equations, (1982), Pitman London · Zbl 1194.35459
[6] Ishii, H., Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open subsets, Bull. fac. sci. eng. chuo univ., 28, 33-77, (1985) · Zbl 0937.35505
[7] Ishii, H., Perron’s method for Hamilton-Jacobi equations, Duke math. J., 55, 369-384, (1987) · Zbl 0697.35030
[8] Barles, G.; Perthame, B., Discontinuous solutions of deterministic optimal stopping time problems, Math. modelling numer. analysis, 21, 557-579, (1987) · Zbl 0629.49017
[9] Lions, P.L.; Souganidis, P.E., Differential games, optimal control and directional derivatives of viscosity solutions of Bellman’s and Isaac’s equations, SIAM J. control optim., 23, 4, (1985) · Zbl 0569.49019
[10] Crandall, M.G.; Ishii, H.; Lions, P.L., User’s guide to viscosity solutions of second-order partial differential equations, Bull. am. math. soc., 27, 1, 1-67, (1992) · Zbl 0755.35015
[11] Barles, G., An approach of deterministic control problems with unbounded controls, Ann. inst. H. Poincaré analyse non linéaire, 7, 4, 235-258, (1990) · Zbl 0717.49021
[12] Evans, L.C., The perturbed test function technique for viscosity solutions of partial differential equations, Proc. R. soc. edinb., 111A, 359-375, (1989) · Zbl 0679.35001
[13] Lasry, J.M.; Lions, P.L., A remark on regularisation in Hilbert space, Israel J. math., 55, 257-266, (1986) · Zbl 0631.49018
[14] Barles, G.; Perthame, B., Exit time problems in optimal control and vanishing viscosity method, SIAM J. control optim., 26, 1133-1148, (1988) · Zbl 0674.49027
[15] Barles G., Soner H. M. & Souganidis P. E., in preparation.
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