Geometric restrictions for the existence of viscosity solutions

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 16, Issue 2, 1999, Pages 189-220

  Cardaliaguet, P ^a   Dacorogna, B ^b   Gangbo, W ^c   Georgy, N ^b  

^a Dept de Mathématiques ^*  (France)

^b EPFL   (Switzerland)

^c GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039374356     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(99)80012-2     Document Type: Article

References (18)

1. J.-P. AUBIN and H. FRANKOWSKA, Set-valued analysis, Birkhäuser, 1991.
2. J.-P. AUBIN, Viability Theory, Birkhäuser, 1992.
3. M. BARDI and I. CAPUZZO DOLCETTA, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Birkhäuser, 1996.
4. G. BARLES, Solutions de viscosité des équations de Hamilton-Jacobi, Springer-Verlag, Berlin, 1994.
5. S.H. BENTON, The Hamilton Jacobi equation. A global approach, Academic Press, New York, 1977.
6. A. BRESSAN and F. FLORES, On total differential inclusions, Rend. Sem. Mat. Univ. Padova, Vol. 92, 1994, pp. 9-16.
7. F.H. CLARKE, Optimization and Nonsmooth Analysis, Wiley Interscience, New York, 1983.
8. M.G. CRANDALL and P.L. LIONS, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., Vol. 277, 1983, pp. 1-4.
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.
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.
11. B. DACOROGNA and P. MARCELLINI, General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases, Acta Mathematics, Vol. 178, 1997, pp. 1-37.
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.
13. W.H. FLEMING and H.M. SONER, Controlled Markov processes and viscosity solution, Springer-Verlag, New York, 1993.
14. H. FRANKOWSKA, Hamilton-Jacobi equations: viscosity solutions and generalized gradients, J. Math. Anal., Vol. 141, 1989, pp. 21-26.
15. H. FRANKOWSKA, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations, SIAM J. Control and Opti., Vol. 31, 1993, pp. 257-272.
16. S.N. KRUZKOV, Generalized solutions of Hamilton-Jacobi equation of eikonal type, USSR Sbornik, Vol. 27, 1975, pp. 406-446.
17. P.L. LIONS, Generalized solution of Hamilton-Jacobi equations, Pitman, London, 1982.
18. R.T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, 1970.