Value functions for Bolza problems with discontinuous lagrangians and Hamilton-Jacobi inequalities
ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 369-393.
@article{COCV_2000__5__369_0,
     author = {Dal Maso, Gianni and Frankowska, Halina},
     title = {Value functions for {Bolza} problems with discontinuous lagrangians and {Hamilton-Jacobi} inequalities},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {369--393},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2000},
     zbl = {0952.49024},
     mrnumber = {1765430},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2000__5__369_0/}
}
TY  - JOUR
AU  - Dal Maso, Gianni
AU  - Frankowska, Halina
TI  - Value functions for Bolza problems with discontinuous lagrangians and Hamilton-Jacobi inequalities
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2000
DA  - 2000///
SP  - 369
EP  - 393
VL  - 5
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/COCV_2000__5__369_0/
UR  - https://zbmath.org/?q=an%3A0952.49024
UR  - https://www.ams.org/mathscinet-getitem?mr=1765430
LA  - en
ID  - COCV_2000__5__369_0
ER  - 
Dal Maso, Gianni; Frankowska, Hélène. Value functions for Bolza problems with discontinuous lagrangians and Hamilton-Jacobi inequalities. ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 369-393. http://www.numdam.org/item/COCV_2000__5__369_0/

[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. | MR 1621319 | Zbl 0917.46025

[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. | MR 1014576 | Zbl 0689.49025

[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. | MR 634239 | Zbl 0484.47034

[4] J.-P. Aubin, A survey of viability theory. SIAM J. Control Optim. 28 ( 1990) 749-788. | MR 1051623 | Zbl 0714.49021

[5] J.-P. Aubin, Viability Theory. Birkhäuser, Boston ( 1991). | MR 1134779 | Zbl 0755.93003

[6] J.-P. Aubin, Optima and Equilibria. Springer-Verlag, Berlin, Grad. Texts in Math. 140 ( 1993). | MR 1217485 | Zbl 0781.90012

[7] J.-P. Aubin and A. Cellina, Differential Inclusions. Springer-Verlag, Berlin, Grundlehren Math. Wiss. 264 ( 1984). | MR 755330 | Zbl 0538.34007

[8] J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis. Wiley & Sons, New York ( 1984). | MR 749753 | Zbl 0641.47066

[9] J.-P. Aubin and H. Frankowska, Set-Valued Analysis. Birkhäuser, Boston ( 1990). | MR 1048347 | Zbl 0713.49021

[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. | MR 1080619 | Zbl 0732.35014

[11] J.W. Bebernes and J.D. Schuur, The Wazewski topological method for contingent equations. Ann. Mat. Pura Appl. 87 ( 1970) 271-280. | MR 299906 | Zbl 0251.34029

[12] G. Buttazzo, Semicontinuity, Relaxation and Integral Representation Problems in the Calculus of Variations. Longman, Harlow, Pitman Res. Notes Math. Ser. ( 1989). | Zbl 0669.49005

[13] L. Cesari, Optimization Theory and Applications. Problems with Ordinary Differential Equations. Springer-Verlag, Berlin, Appl. Math. 17 ( 1983). | MR 688142 | Zbl 0506.49001

[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. | MR 690039 | Zbl 0599.35024

[16] G. Dal Maso and L. Modica, Integral functionals determined by their minima. Rend. Sem. Mat. Univ. Padova 76 ( 1986) 255-267. | Numdam | MR 881574 | Zbl 0613.49028

[17] C. Dellacherie, P.-A. Meyer, Probabilités et potentiel. Hermann, Paris ( 1975). | MR 488194 | Zbl 0323.60039

[18] H. Frankowska, L'équation d'Hamilton-Jacobi contingente. C. R. Acad. Sci. Paris Sér. I Math. 304 ( 1987) 295-298. | MR 886727 | Zbl 0612.49023

[19] H. Frankowska, Optimal trajectories associated to a solution of contingent Hamilton-Jacobi equations. Appl. Math. Optim. 19 ( 1989) 291-311. | MR 974188 | Zbl 0672.49023

[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. | MR 1200233 | Zbl 0796.49024

[22] H. Frankowska, S. Plaskacz and T. Rzeżuchowski, Measurable viability theorems and Hamilton-Jacobi-Bellman equation. J. Differential Equations 116 ( 1995) 265-305. | MR 1318576 | Zbl 0836.34016

[23] G.N. Galbraith, Extended Hamilton-Jacobi characterization of value functions in optimal control. Preprint Washington University, Seattle ( 1998). | MR 1780920

[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. | MR 806060 | Zbl 0593.90095

[25] A.D. Ioffe, On lower semicontinuity of integral functionals. SIAM J. Control Optim. 15 ( 1977) 521-521 and 991-1000. | MR 637235 | Zbl 0379.46022

[26] C. Olech, Weak lower semicontinuity of integral functionals. J. Optim. Theory Appl. 19 ( 1976) 3-16. | MR 428161 | Zbl 0305.49019

[27] T. Rockafellar, Proximal subgradients, marginal values and augmented Lagrangians in nonconvex optimization. Math. Oper. Res. 6 ( 1981) 424-436. | MR 629642 | Zbl 0492.90073

[28] T. Rockafellar and R. Wets, Variational Analysis. Springer-Verlag, Berlin, Grundlehren Math. Wiss. 317 ( 1998). | MR 1491362 | Zbl 0888.49001

[29] A.I. Subbotin, A generalization of the basic equation of the theory of the differential games. Soviet. Math. Dokl. 22 ( 1980) 358-362. | Zbl 0467.90095