Free access
Issue
ESAIM: COCV
Volume 5, 2000
Page(s) 369 - 393
DOI http://dx.doi.org/10.1051/cocv:2000114
Published online 15 August 2002
  1. M. Amar, G. Bellettini and S. Venturini, Integral representation of functionals defined on curves of W1,p. Proc. Roy. Soc. Edinburgh Sect. A 128 (1998) 193-217. [MathSciNet]
  2. L. Ambrosio, O. Ascenzi and G. Buttazzo, Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands. J. Math. Anal. Appl. 142 (1989) 301-316. [CrossRef] [MathSciNet]
  3. J.-P. Aubin, Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions. Advances in Mathematics, Supplementary Studies, edited by L. Nachbin (1981) 160-232.
  4. J.-P. Aubin, A survey of viability theory. SIAM J. Control Optim. 28 (1990) 749-788. [CrossRef] [MathSciNet]
  5. J.-P. Aubin, Viability Theory. Birkhäuser, Boston (1991).
  6. J.-P. Aubin, Optima and Equilibria. Springer-Verlag, Berlin, Grad. Texts in Math. 140 (1993).
  7. J.-P. Aubin and A. Cellina, Differential Inclusions. Springer-Verlag, Berlin, Grundlehren Math. Wiss. 264 (1984).
  8. J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis. Wiley & Sons, New York (1984).
  9. J.-P. Aubin and H. Frankowska, Set-Valued Analysis. Birkhäuser, Boston (1990).
  10. E.N. Barron and R. Jensen, Semicontinuous viscosity solutions for Hamilton-Jacobi equations with convex Hamiltonian. Comm. Partial Differential Equations 15 (1990) 1713-1742. [MathSciNet]
  11. J.W. Bebernes and J.D. Schuur, The Wazewski topological method for contingent equations. Ann. Mat. Pura Appl. 87 (1970) 271-280. [CrossRef] [MathSciNet]
  12. G. Buttazzo, Semicontinuity, Relaxation and Integral Representation Problems in the Calculus of Variations. Longman, Harlow, Pitman Res. Notes Math. Ser. (1989).
  13. L. Cesari, Optimization Theory and Applications. Problems with Ordinary Differential Equations. Springer-Verlag, Berlin, Appl. Math. 17 (1983).
  14. B. Cornet, Regular properties of tangent and normal cones. Cahiers de Maths. de la Décision No. 8130 (1981).
  15. M.G. Crandall, P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277 (1983) 1-42. [CrossRef] [MathSciNet]
  16. G. Dal Maso and L. Modica, Integral functionals determined by their minima. Rend. Sem. Mat. Univ. Padova 76 (1986) 255-267. [MathSciNet]
  17. C. Dellacherie, P.-A. Meyer, Probabilités et potentiel. Hermann, Paris (1975).
  18. H. Frankowska, L'équation d'Hamilton-Jacobi contingente. C. R. Acad. Sci. Paris Sér. I Math. 304 (1987) 295-298.
  19. H. Frankowska, Optimal trajectories associated to a solution of contingent Hamilton-Jacobi equations. Appl. Math. Optim. 19 (1989) 291-311. [CrossRef] [MathSciNet]
  20. H. Frankowska, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations, in Proc. of IEEE CDC Conference. Brighton, England (1991).
  21. H. Frankowska, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 31 (1993) 257-272. [CrossRef] [MathSciNet]
  22. H. Frankowska, S. Plaskacz and T. Rzezuchowski, Measurable viability theorems and Hamilton-Jacobi-Bellman equation. J. Differential Equations 116 (1995) 265-305. [CrossRef] [MathSciNet]
  23. G.N. Galbraith, Extended Hamilton-Jacobi characterization of value functions in optimal control. Preprint Washington University, Seattle (1998).
  24. H.G. Guseinov, A.I. Subbotin and. V.N. Ushakov, Derivatives for multivalued mappings with application to game-theoretical problems of control. Problems Control Inform. 14 (1985) 155-168.
  25. A.D. Ioffe, On lower semicontinuity of integral functionals. SIAM J. Control Optim. 15 (1977) 521-521 and 991-1000. [CrossRef]
  26. C. Olech, Weak lower semicontinuity of integral functionals. J. Optim. Theory Appl. 19 (1976) 3-16. [CrossRef]
  27. T. Rockafellar, Proximal subgradients, marginal values and augmented Lagrangians in nonconvex optimization. Math. Oper. Res. 6 (1981) 424-436. [CrossRef] [MathSciNet]
  28. T. Rockafellar and R. Wets, Variational Analysis. Springer-Verlag, Berlin, Grundlehren Math. Wiss. 317 (1998).
  29. A.I. Subbotin, A generalization of the basic equation of the theory of the differential games. Soviet. Math. Dokl. 22 (1980) 358-362.