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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2183))

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References

  1. Bardi, M., Capuzzo-Dolcetta, I.: Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA (1997)

    Book  MATH  Google Scholar 

  2. Barles, G.: Solutions de Viscosité des Équations de Hamilton-Jacobi. Mathématiques & Applications (Berlin), vol. 17. Springer, Paris (1994)

    Google Scholar 

  3. Barron, E.N., Jensen, R.: Semicontinuous viscosity solutions for Hamilton-Jacobi equations with convex Hamiltonians. Commun. Partial Differ. Equ. 15(12), 1713–1742 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cannarsa, P., Sinestrari, C.: Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control. Progress in Nonlinear Differential Equations and their Applications, vol. 58. Birkhäuser, Boston (2002)

    Google Scholar 

  5. Crandall, M.G., Lions, P.-L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 277, 1–42 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  6. Crandall, M.G., Evans, L.C., Lions, P.-L.: Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 282, 487–502 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  7. Crandall, M.G., Ishii, H., Lions, P.-L.: User’s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. (N.S.) 27(1), 1–67 (1992)

    Google Scholar 

  8. Evans, L.C.: Partial Differential Equations, 2nd edn. Graduate Studies in Mathematics, vol. 19. American Mathematical Society, Providence, RI (2010)

    Google Scholar 

  9. Evans, L.C.: Adjoint and compensated compactness methods for Hamilton–Jacobi PDE. Arch. Ration. Mech. Anal. 197, 1053–1088 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Fleming, W.H., Soner, H.M.: Controlled Markov Processes and Viscosity Solutions. Stochastic Modelling and Applied Probability, vol. 25. Springer, New York (2006)

    Google Scholar 

  11. Giga, Y.: Surface Evolution Equations. A Level Set Approach. Monographs in Mathematics, vol. 99, xii+264pp. Birkhäuser, Basel, Boston, Berlin (2006)

    Google Scholar 

  12. Ishii, H.: Perron’s method for Hamilton–Jacobi equations. Duke Math. J. 55(2), 369–384 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kružkov, S.N.: Generalized solutions of nonlinear equations of the first order with several independent variables. II. Mat. Sb. (N.S.) (Russian) 72(114), 108–134 (1967)

    Google Scholar 

  14. Lions, P.-L.: Generalized Solutions of Hamilton-Jacobi Equations. Research Notes in Mathematics, vol. 69. Pitman, Boston, MA, London (1982)

    Google Scholar 

  15. Nisio, M.: Stochastic Control Theory: Dynamic Programming Principle. Probability Theory and Stochastic Modelling, vol. 72, xvi+250 pp. Springer, Tokyo (2015)

    Google Scholar 

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Le, N.Q., Mitake, H., Tran, H.V. (2017). Appendix of Part II. In: Mitake, H., Tran, H. (eds) Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations. Lecture Notes in Mathematics, vol 2183. Springer, Cham. https://doi.org/10.1007/978-3-319-54208-9_7

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