Value functions for Bolza problems with discontinuous lagrangians and Hamilton-Jacobi inequalities

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1. [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. Zbl0917.46025MR1621319
2. [2] L. Ambrosio, O. Ascenzi and G. Buttazzo, Lipschitz regularity for minimizers of integral functionals with highly discontinuons integrands. J. Math. Anal. Appl. 142 ( 1989) 301-316. Zbl0689.49025MR1014576
3. [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. Zbl0484.47034MR634239
4. [4] J.-P. Aubin, A survey of viability theory. SIAM J. Control Optim. 28 ( 1990) 749-788. Zbl0714.49021MR1051623
5. [5] J.-P. Aubin, Viability Theory. Birkhäuser, Boston ( 1991). Zbl0755.93003MR1134779
6. [6] J.-P. Aubin, Optima and Equilibria. Springer-Verlag, Berlin, Grad. Texts in Math. 140 ( 1993). Zbl0781.90012MR1217485
7. [7] J.-P. Aubin and A. Cellina, Differential Inclusions. Springer-Verlag, Berlin, Grundlehren Math. Wiss. 264 ( 1984). Zbl0538.34007MR755330
8. [8] J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis. Wiley & Sons, New York ( 1984). Zbl0641.47066MR749753
9. [9] J.-P. Aubin and H. Frankowska, Set-Valued Analysis. Birkhäuser, Boston ( 1990). Zbl0713.49021MR1048347
10. [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. Zbl0732.35014MR1080619
11. [11] J.W. Bebernes and J.D. Schuur, The Wazewski topological method for contingent equations. Ann. Mat. Pura Appl. 87 ( 1970) 271-280. Zbl0251.34029MR299906
12. [12] G. Buttazzo, Semicontinuity, Relaxation and Integral Representation Problems in the Calculus of Variations. Longman, Harlow, Pitman Res. Notes Math. Ser. ( 1989). Zbl0669.49005
13. [13] L. Cesari, Optimization Theory and Applications. Problems with Ordinary Differential Equations. Springer-Verlag, Berlin, Appl. Math. 17 ( 1983). Zbl0506.49001MR688142
14. [14] B. Cornet, Regular properties of tangent and normal cones. Cahiers de Maths, de la Décision No. 8130 ( 1981). 
15. [15] M.G. Crandall, P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277 ( 1983) 1-42. Zbl0599.35024MR690039
16. [16] G. Dal Maso and L. Modica, Integral functionals determined by their minima. Rend. Sem. Mat. Univ. Padova 76 ( 1986) 255-267. Zbl0613.49028MR881574
17. [17] C. Dellacherie, P.-A. Meyer, Probabilités et potentiel. Hermann, Paris ( 1975). Zbl0323.60039MR488194
18. [18] H. Frankowska, L'équation d'Hamilton-Jacobi contingente. C. R. Acad. Sci. Paris Sér. I Math. 304 ( 1987) 295-298. Zbl0612.49023MR886727
19. [19] H. Frankowska, Optimal trajectories associated to a solution of contingent Hamilton-Jacobi equations. Appl. Math. Optim. 19 ( 1989) 291-311. Zbl0672.49023MR974188
20. [20] H. Frankowska, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations, in Proc. of IEEE CDC Conference. Brighton, England ( 1991). Zbl0796.49024
21. [21] H. Frankowska, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 31 ( 1993) 257-272. Zbl0796.49024MR1200233
22. [22] H. Frankowska, S. Plaskacz and T. Rzeżuchowski, Measurable viability theorems and Hamilton-Jacobi-Bellman equation. J. Differential Equations 116 ( 1995) 265-305. Zbl0836.34016MR1318576
23. [23] G.N. Galbraith, Extended Hamilton-Jacobi characterization of value functions in optimal control. Preprint Washington University, Seattle ( 1998). Zbl0971.49017MR1780920
24. [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 ( 1985155-168. Zbl0593.90095MR806060
25. [25] A.D. Ioffe, On lower semicontinuity of integral functionals. SIAM J. Control Optim. 15 ( 1977) 521-521 and 991-1000. Zbl0379.46022MR637235
26. [26] C. Olech, Weak lower semicontinuity of integral functionals. J. Optim. Theory Appl. 19 ( 1976) 3-16. Zbl0305.49019MR428161
27. [27] T. Rockafellar, Proximal subgradients, marginal values and augmented Lagrangians in nonconvex optimization. Math. Oper. Res. 6 ( 1981) 424-436. Zbl0492.90073MR629642
28. [28] T. Rockafellar and R. Wets, Variational Analysis. Springer-Verlag, Berlin, Grundlehren Math. Wiss. 317 ( 1998). Zbl0888.49001MR1491362
29. [29] A.I. Subbotin, A generalization of the basic equation of the theory of the differential games. Soviet. Math. Dokl. 22 ( 1980) 358-362. Zbl0467.90095

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