On the generalized Dirichlet problem for viscous Hamilton-Jacobi equations

Journal des Mathematiques Pures et Appliquees

Volumn 83, Issue 1, 2004, Pages 53-75

  Barles, Guy ^a   Da Lio, Francesca ^b  

^a UNIVERSITÉ DE TOURS   (France)

^b UNIVERSITY OF TURIN   (Italy)

Author keywords

Generalized Dirichlet problem; Geometric equations; Maximum principle; Semilinear elliptic equations; State constraint boundary conditions; Viscosity solutions; Viscous Hamilton Jacobi equations

Indexed keywords

EID: 0347568271     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-7824(03)00070-9     Document Type: Article

References (28)

1. Amour L. Ben-Artzi M. Global existence and decay for viscous Hamilton-Jacobi equations Nonlinear Anal. 31 5-6 1998 621 628
2. Bardi M. Capuzzo Dolcetta I. Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations 1997 Birkhäuser Boston
3. Barles G. Solutions de Viscosite des Equations de Hamilton-Jacobi. Collection Math. Appl. SMAI vol. 17 1994 Springer-Verlag
4. Barles G. Nonlinear Neumann boundary conditions for quasilinear degenerate elliptic equations and applications J. Differential Equations 154 1999 191-224
5. Barles G. Burdeau J. The Dirichlet problem for semilinear second-order degenerate elliptic equations and applications to stochastic exit time control problems Comm. Partial Differential Equations 20 1-2 1995 129-178
6. G. Barles, F. Da Lio, Remarks on the Dirichlet and state-constraint problems for quasilinear parabolic equations, Adv. Differential Equations, in press
7. Barles G. Perthame B. Comparison principle for Dirichlet type Hamilton-Jacobi equations and singular perturbations of degenerated elliptic equations Appl. Math. Opt. 21 1990 21-44
8. Barles G. Rouy E. A strong comparison result for the Bellman equation arising in stochastic exit time control problems and its applications Comm. Partial Differential Equations 23 11-12 1998 1995-2033
9. Barles G. Rouy E. Souganidis P.E. Remarks on the Dirichlet problem for quasilinear elliptic and parabolic equations A Volume in Honor of W.H. Fleming in: McEneaney W.M. Yin G.G. Zhang Q. (Eds.), Stochastic Analysis, Control, Optimization and Applications 1999 209-222 Birkhäuser Boston
10. Ben-Artzi M. Global existence and decay for a nonlinear parabolic equations Nonlinear Anal. 19 1992 763-768
11. Ben-Artzi M. Global properties of some nonlinear parabolic equations. Nonlinear partial differential equations and their applications Collège de France Seminar, Vol. XIV, Paris, 1997/1998 Stud. Math. Appl. vol. 31 2002 57 67 North-Holland Amsterdam
12. Ben-Artzi M. Souplet Ph. Weissler F. The local theory for viscuous Hamilton-Jacobi equations in Lebesgue spaces J. Math. Pures Appl. 81 2002 343-378
13. Capuzzo Dolcetta I. Lions P.-L. Hamilton-Jacobi equations with state constraints Trans. Amer. Math. Soc. 318 2 1990 643-683
14. Crandall M.G. Ishii H. Lions P.-L. User's guide to viscosity solutions of second order Partial differential equations Bull. Amer. Soc. 27 1992 1-67
15. Da Lio F. Strong comparison results for quasilinear equations in annular domains and applications Comm. Partial Differential Equations 27 1-2 2002 283-323
16. Fila M. Lieberman G. Derivative blow-up and beyond for quasilinear parabolic equation Differential Integral Equations 7 3 1994 811-821
17. Fleming W.H. Soner H.M. Controlled Markov Processes and Viscosity Solutions Appl. Math. 1993 Springer-Verlag New-York
18. Gilbarg D. Trudinger N.S. Elliptic Partial Differential Equations of Second-Order 1983 Springer-Verlag New-York
19. q, Preprint
20. Ishii H. Perron's method for Hamilton-Jacobi equations Duke Math. J. 55 1987 369-384
21. Ishii H. Fully nonlinear oblique derivative problems for nonlinear second-order elliptic PDE's Duke Math. J. 62 1991 663-691
22. Katsoulakis M. Viscosity solutions of 2nd order fully nonlinear elliptic equations with state constraints Indiana Univ. Math. J. 43 2 1994 493-519
23. Ladyzhenskaya O.A. Ural'tseva N.N. Linear and Quasilinear Elliptic Equations 1968 Academic Press
24. O.A. Ladyzhenskaya, V.A. Solonokov, N.N. Ural'tseva, Linear and quasilinear equations of parabolic type, Trans. Amer. Math. Soc. 23
25. Lasry J.M. Lions P.-L. Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints Math. Ann. 283 1989 583-630
26. Lions P.-L. Résolution de problèmes elliptiques quasilinéaires Arch. Rational Mech. Anal. 74 4 1980 335-353 (French)
27. Soner M.H. Optimal control problems with state-space constraints SIAM J. Control Optim. 24 1986 Part I: 552-562, Part II: 1110-1122
28. Souplet Ph. Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions Differential Integral Equations 15 2 2002 237-256