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All issues Volume 28 (2022) ESAIM: COCV, 28 (2022) 55 References
Open Access
Issue
ESAIM: COCV
Volume 28, 2022
Article Number 55
Number of page(s) 32
DOI https://doi.org/10.1051/cocv/2022051
Published online 18 August 2022
  1. J.-P. Aubin, Viability Theory. Birkhäuser, Boston-Basel-Berlin (1991). [Google Scholar]
  2. J.-P. Aubin and H. Frankowska, Set-Valued Analysis. Birkhäuser, Boston-Basel-Berlin (1990). [Google Scholar]
  3. M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkhäuser, Boston (1997). [Google Scholar]
  4. G. Barles, Discontinuous viscosity solutions of first-order Hamilton-Jacobi equations: a guided visit. Nonlinear Anal. 20 (1993) 1123–1134. [CrossRef] [MathSciNet] [Google Scholar]
  5. E.N. Barron and R. Jensen, Semicontinuous viscosity solutions for Hamilton-Jacobi equations with convex Hamiltonians. Commun. Partial Differ. Equ. 15 (1990) 1713–1742. [Google Scholar]
  6. E.N. Barron and R. Jensen, Optimal control and semicontinuous viscosity solutions. Proc. Am,. Math. Soc. 113 (1991) 397–402. [CrossRef] [Google Scholar]
  7. J. Bernis and P. Bettiol, Solutions to the Hamilton-Jacobi equation for Bolza problems with discontinuous time dependent data. ESAIM: COCV 26 (2020) 35 pages. [CrossRef] [EDP Sciences] [Google Scholar]
  8. P. Bettiol and R.B. Vinter, The Hamilton Jacobi equation for optimal control problems with discontinuous time dependence. SIAM J. Control Optim. 55 (2017) 1199–1225. [CrossRef] [MathSciNet] [Google Scholar]
  9. P. Cannarsa and C. Sinestrari, Semiconcave functions, Hamilton-Jacobi equations, and optimal control. Vol. 58 of Progress in Nonlinear Differential Equations and their Applications. Birkhauser, Boston (2004). [Google Scholar]
  10. L. Cesari, Optimization-theory and applications, problems with ordinary differential equations. Springer, New York (1983). [Google Scholar]
  11. M.G. Crandall and P.-L. Lions, Remarks on the existence and uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations. Illinois J. Math. 31 (1987) 665–688. [CrossRef] [MathSciNet] [Google Scholar]
  12. G. Dal Maso and H. Frankowska, Value functions for Bolza problems with discontinuous Lagrangians and Hamilton-Jacobi inequalities. ESAIM: COCV 5 (2000) 369–393. [CrossRef] [EDP Sciences] [Google Scholar]
  13. H. Frankowska, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 31 (1993) 257–272. [Google Scholar]
  14. H. Frankowska and M. Mazzola, Discontinuous solutions of Hamilton-Jacobi-Bellman equation under state constraints. Calc. Var. Partial Differ. Equ. 46 (2013) 725–747. [CrossRef] [Google Scholar]
  15. H. Frankowska, S. Plaskacz and T. Rzezuchowski, Measurable viability theorems and Hamilton-Jacobi-Bellman equation. J. Differ. Equ. 116 (1995) 265–305. [CrossRef] [Google Scholar]
  16. G.H. Galbraith, Extended Hamilton-Jacobi characterization of value functions in optimal control. SIAM J. Control Optim. 39 (2000) 281–305. [CrossRef] [MathSciNet] [Google Scholar]
  17. J.W. Hagood and B.S. Thomson, Recovering a function from a Dini derivative. Amer. Math. Monthly 113 (2006) 34–46. [CrossRef] [MathSciNet] [Google Scholar]
  18. H. Ishii, Uniqueness of unbounded solutions of Hamilton-Jacobi equations. Indiana Univ. Math. J. 33 (1984) 721–748. [CrossRef] [MathSciNet] [Google Scholar]
  19. H. Ishii, A generalization of a theorem of Barron and Jensen and a comparison theorem for lower semicontinuous viscosity solutions. Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 137–154. [CrossRef] [MathSciNet] [Google Scholar]
  20. A. Misztela, The value function representing Hamilton-Jacobi equation with Hamiltonian depending on value of solution. ESAIM: COCV 20 (2014) 771–802. [CrossRef] [EDP Sciences] [Google Scholar]
  21. A. Misztela, On nonuniqueness of solutions of Hamilton-Jacobi-Bellman equations. Appl. Math. Optim. 77 (2018) 599–611. [CrossRef] [MathSciNet] [Google Scholar]
  22. A. Misztela, Representation of Hamilton-Jacobi equation in optimal control theory with compact control set. SIAM J. Control Optim. 57 (2019) 53–77. [CrossRef] [MathSciNet] [Google Scholar]
  23. A. Misztela, Representation of Hamilton-Jacobi equation in optimal control theory with unbounded control set. J. Optim. Theory Appl. 185 (2020) 361–383. [CrossRef] [MathSciNet] [Google Scholar]
  24. A. Misztela and S. Plaskacz, An initial condition reconstruction in Hamilton-Jacobi equations. Nonlinear Anal. 200 (2020), 15 pages. [Google Scholar]
  25. A. Plaksin, Viscosity Solutions of Hamilton-Jacobi-Bellman-Isaacs equations for time-delay systems. SIAM J. Control Optim. 59 (2021) 1951–1972. [CrossRef] [MathSciNet] [Google Scholar]
  26. S. Plaskacz and M. Quincampoix, On representation formulas for Hamilton Jacobi's equations related to calculus of variations problems. Topol. Methods Nonlinear Anal. 20 (2002) 85–118. [CrossRef] [MathSciNet] [Google Scholar]
  27. F. Rampazzo, C. Sartori, Hamilton-Jacobi-Bellman equations with fast gradient-dependence. Indiana Univ. Math. J. 49 (2000) 1043–1077. [CrossRef] [Google Scholar]
  28. R.T. Rockafellar, Optimal arcs and the minimum value function in problems of Lagrange. Trans. Amer. Math. Soc. 180 (1973) 53–84. [CrossRef] [MathSciNet] [Google Scholar]
  29. R.T. Rockafellar, Existence theorems for general control problems of Bolza and Lagrange. Adv. Math. 15 (1975) 312–333. [CrossRef] [Google Scholar]
  30. R.T. Rockafellar and R.J.-B. Wets, Variational Analysis. Springer-Verlag, Berlin (1998). [Google Scholar]

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