Geometric restrictions for the existence of viscosity solutions
Cardaliaguet, P. ; Dacorogna, B. ; Gangbo, W. ; Georgy, N.
Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999), p. 189-220 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1999-01-01
@article{AIHPC_1999__16_2_189_0,
     author = {Cardaliaguet, P. and Dacorogna, Bernard and Gangbo, W. and Georgy, N.},
     title = {Geometric restrictions for the existence of viscosity solutions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {16},
     year = {1999},
     pages = {189-220},
     mrnumber = {1674769},
     zbl = {0927.35021},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1999__16_2_189_0}
}

Cardaliaguet, P.; Dacorogna, B.; Gangbo, W.; Georgy, N. Geometric restrictions for the existence of viscosity solutions. Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) pp. 189-220. http://gdmltest.u-ga.fr/item/AIHPC_1999__16_2_189_0/

[1] J.-P. Aubin and H. Frankowska, Set-valued analysis, Birkhäuser, 1991.

[2] J.-P. Aubin, Viability Theory, Birkhäuser, 1992. | MR 1134779 | Zbl 0755.93003

[3] M. Bardi and I. Capuzzo Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Birkhäuser, 1996. | MR 1484411 | Zbl 0890.49011

[4] G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi, Springer-Verlag, Berlin, 1994. | MR 1613876 | Zbl 0819.35002

[5] S.H. Benton, The Hamilton Jacobi equation. A global approach, Academic Press, New York, 1977. | MR 442431 | Zbl 0418.49001

[6] A. Bressan and F. Flores, On total differential inclusions, Rend. Sem. Mat. Univ. Padova, Vol. 92, 1994, pp. 9-16. | Numdam | MR 1320474 | Zbl 0821.35158

[7] F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley Interscience, New York, 1983. | MR 709590 | Zbl 0582.49001

[8] M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., Vol. 277, 1983, pp. 1-4. | MR 690039 | Zbl 0599.35024

[9] B. Dacorogna and P. Marcellini, Théorèmes d'existence dans le cas scalaire et vectoriel pour les équations de Hamilton-Jacobi, C.R. Acad. Sci. Paris, t. 322, Série I, 1996, pp. 237-240. | MR 1378259 | Zbl 0846.35028

[10] B. Dacorogna and P. Marcellini, Sur le Problème de Cauchy-Dirichlet pour les systèmes d'équations non linéaires du premier ordre, C.R. Acad. Sci. Paris, t. 323, Série I, 1996, pp. 599-602. | MR 1411049 | Zbl 0860.35020

[11] B. Dacorogna and P. Marcellini, General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases, Acta Mathematica, Vol. 178, 1997, pp. 1-37. | MR 1448710 | Zbl 0901.49027

[12] A. Douglis, The continuous dependence of generalized solutions of non linear partial differential equations upon initial data, Comm. Pure Appl. Math., Vol. 14, 1961, pp. 267-284. | MR 139848 | Zbl 0117.31102

[13] W.H. Fleming and H.M. Soner, Controlled Markov processes and viscosity solution, Springer-Verlag, New York, 1993. | MR 1199811 | Zbl 0773.60070

[14] H. Frankowska, Hamilton-Jacobi equations: viscosity solutions and generalized gradients, J. Math. Anal., Vol. 141, 1989, pp. 21-26. | MR 1004581 | Zbl 0727.35028

[15] H. Frankowska, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations, SIAM J. Control and Opti., Vol. 31, 1993, pp. 257-272. | MR 1200233 | Zbl 0796.49024

[16] S.N. Kruzkov, Generalized solutions of Hamilton-Jacobi equation of eikonal type, USSR Sbornik, Vol. 27, 1975, pp. 406-446. | Zbl 0369.35012

[17] P.L. Lions, Generalized solution of Hamilton-Jacobi equations, Pitman, London, 1982. | MR 667669 | Zbl 0497.35001

[18] R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970. | MR 274683 | Zbl 0193.18401