Generalized solutions by Cauchy's method of characteristics
Rendiconti del Seminario Matematico della Università di Padova, Tome 77 (1987), pp. 317-350. 
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     author = {Miric\u{a}, \c{S}tefan},
     title = {Generalized solutions by {Cauchy's} method of characteristics},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {317--350},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {77},
     year = {1987},
     mrnumber = {904627},
     zbl = {0627.49015},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_1987__77__317_0/}
}
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Mirică, Ştefan. Generalized solutions by Cauchy's method of characteristics. Rendiconti del Seminario Matematico della Università di Padova, Tome 77 (1987), pp. 317-350. http://www.numdam.org/item/RSMUP_1987__77__317_0/

[1] R. Abraham - J. ROBBIN, Transversal Mappings and Flows, Benjamin, New York, 1967. | MR | Zbl

[2] S.H. Benton jr., The Hamilton-Jacobi equation. A global approach, Academic Press, New York, 1977. | MR | Zbl

[3] V.G. Boltyanskii, Mathematical Methods of Optimal Control, Holt, Rinehart & Winston, New York, 1971. | MR | Zbl

[4] P. Brunovsky, Existence of regular synthesis for general control problems, J. Differential Equations, 38 (1980), pp. 317-343. | MR | Zbl

[5] L. Cesari, Optimization. Theory and Applications, Springer, New York, 1983. | MR | Zbl

[6] F.H. Clarke, Optimal control and the true hamiltonian, SIAM Review, 21 (1979), pp. 157-166. | MR | Zbl

[7] R. Courant - D. Hilbert, Methods of Mathematical Physics, vol. II, Wiley, New York, 1962. | MR | Zbl

[8] M.G. Crandal - L.C. Evans - P.L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. A.M.S., 282, 2 (1984), pp. 487-502. | MR | Zbl

[9] R.P. Fedorenko, On the Cauchy problem for Bellman equation of dynamic programming, Z. Vyc. Mat. i Mat. Phys., 9 (1969), pp. 426-432 (Russian). | MR | Zbl

[10] W.H. Fleming, The Cauchy problem for a nonlinear first order partial differential equation, J. Differential Equations, 5 (1969), pp . 515-530. | MR | Zbl

[11] A. Halanay, Differential Equations, Ed. Did. Pedagogică, Bucuresti, 1972 (Romanian). | MR

[12] Ph. Hartman, Ordinary Differential Equations, Wiley, New York, 1964. | MR | Zbl

[13] R. Isaacs, Differential Games, Wiley, New York, 1965. | MR | Zbl

[14] S. Lang, Introduction to Differentiable Manifolds, Interscience, New York, 1962. | MR | Zbl

[15] P.L. Lions, Generalized Solutions of Hamilton-Jacobi Equations, Pitman, Boston, 1982. | MR | Zbl

[16] J. Mather, Stratifications and Mappings, Preprint, Harvard University (Russian transl.: Uspehi Mat. Nauk, 27 (1972), pp. 85-118). | MR | Zbl

[17] Ş. Miric, The contingent and the paratingent as generalized derivatives for vector-valued and set-valued mappings, Nonlinear Analysis. Theory, Theory & Appl., 6 (1982), pp. 1335-1368. | MR | Zbl

[18] Ş. Miric, Stratified Hamiltonians and the optimal feedback control, Ann. Mat. Pura Appl., 33 (1983), pp. 51-78. | MR | Zbl

[19] Ş. Miric, Stratified Hamilton-Jacobi equations and applications, Anal. Univ. Bucureşti, Seria Mat., 33 (1984), pp. 59-68. | MR | Zbl

[20] Ş Mirică, Dynamic programming method for stratified optimal control problems, Preprint Series in Mathematics, No. 12/1984, Increst-Inst. Inst. Mat., Bucureşti, 1984.

[21] H. Stalford, Sufficiency theorem for discontinuous optimal cost surfaces, SIAM J. Control Opt., 16 (1978), pp. 63-82. | MR | Zbl

[22] H. Sussman, Analytic stratifications and control theory, « Proc. Int. Congress of Math. » (Helsinki, 1978), pp. 865-871. | MR | Zbl

[23] M. Tamm, Subanalytic sets in the Calculus of Variations, Acta Math., 146 (1981), pp. 167-199. | MR | Zbl

[24] R. Thom, Ensembles et morphismes stratifiés, Bull. Amer. Math. Soc., 75 (1969), pp. 24-284. | MR | Zbl

[25] E. Whitney, Tangents to an analytic variety, Ann. of Math., 81 (1965), pp. 496-549. | MR | Zbl