Existence and comparison results for fully nonlinear degenerate elliptic equations without zeroth-order term

Communications in Partial Differential Equations

Volumn 26, Issue 11-12, 2001, Pages 2323-2337

  Barles, G ^a   Busca, Jérôme ^a  

^a UNIVERSITÉ DE TOURS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038359246     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1081/PDE-100107824     Document Type: Review

References (17)

1. Bardi, M.; Capuzzo Dolcetta, I. Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Birkhäuser, Boston, 1997.
2. Bardi, M.; Da Lio, F. On the strong maximum principle for fully nonlinear degenerate elliptic equations. Arch. Math. 1999, 73, 276-285.
3. Barles, G. Solutions de viscosite des equations de Hamilton-Jacobi. Collection "Mathematiques et Applications" de la SMAI, no17, Springer-Verlag (1994).
4. Barles, G.; Burdeau, J. The Dirichlet problem for semilinear second-order degenerate elliptic equations and applications to stochastic exit time control problems. Comm. in P.D.E. 1995, 20 (1&2), 129-178.
5. Barles, G.; Murat, F. The Maximum Principle for quasilinear elliptic equations with quadratic growth conditions. Arch. Rational Mech. Anal. 1995, 133, 77-101.
6. Barles, G.; Rouy, E. A strong comparison result for the bellman equation arising in stochastic exit time control problems and its applications. Comm. in PDE, 1998, 23 (11&12), 1995-2033.
7. Barles, G.; Rouy, E.; Souganidis, P.E. Remarks on the Dirichlet problem for quasilinear elliptic and parabolic equations. In "Stochastic Analysis, Control, Optimization and Applications. A Volume in Honor of W.H. Fleming", McEneaney, W.M.; Yin, G.G.; Zhang, Q. eds. pp. 209-222, Birkhäuser, Boston, 1999.
8. Crandall, M.G.; Lions, P.L. Viscosity solutions of Hamilton-Jacobi Equations, Trans. Amer. Math. Soc. 1983, 277, 1-42.
9. Crandall, M.G.; Evans, L.C.; Lions, P.L. Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 1984, 282, 487-502.
10. Crandall, M.G.; Ishii, H.; Lions, P.-L. User's guide to viscosity solutions of second order partial differential equations, Bull. AMS 1992, 27, 1-67.
11. Da Lio, F. A Strong Comparison Result for Quasilinear Equations in Bounded Annular Domains and Applications. Preprint.
12. Fleming, W.H.; Soner, H.M. Controlled markov processes and viscosity solutions. Applications of Mathematics, Springer-Verlag, New York, 1993.
13. Gilbarg, D.; Trudinger, N.S. Elliptic Partial Differential Equations of Second-Order. Springer, New York, 1983.
14. Ishii, H. Perron's Method for Hamilton-Jacobi Equations. Duke Math. J. 1987, 55, 369-384.
15. Jensen, R. Uniqueness of Lipschitz extensions minimizing the supnorm of the gradient, Arch. Rat. Mech. Anal. 1993, 123, 51-74.
16. Juutinen, P.; Lindqvist, P.; Manfredi, J.J. The ∞-eigenvalue problem. Arch. Rat. Mech. Anal. 1999, 148, 89-105.
17. Ladyzhenskaya, O.A.; Ural'tseva, N.N. Linear and Quasilinear Elliptic Equations, Academic Press, 1968.