Volume 12, Number 2, April 2006
|Page(s)||216 - 230|
|Published online||22 March 2006|
- M. Bardi, A boundary value problem for the minimum-time function. SIAM J. Control Optim. 27 (1989) 776–785. [CrossRef] [MathSciNet]
- M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkhäuser (1997).
- M. Bardi and P. Soravia, Hamilton-Jacobi equations with a singular boundary condition on a free boundary and applications to differential games. Trans. Amer. Math. Soc. 325 (1991) 205–229. [CrossRef] [MathSciNet]
- G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. Springer-Verlag (1994).
- G. Barles and B. Perthame, Discontinuous solutions of deterministic optimal stopping time problems. RAIRO: M2AN 21 (1987) 557–579.
- L. Caffarelli, M.G. Crandall, M. Kocan and A. Swiech, On viscosity solutions of fully nonlinear equations with measurable ingredients. Comm. Pure Appl. Math. 49 (1996) 365–397. [CrossRef] [MathSciNet]
- F. Camilli and A. Siconolfi, Hamilton-Jacobi equations with measurable dependence on the state variable. Adv. Differential Equations 8 (2003) 733–768. [MathSciNet]
- I. Capuzzo Dolcetta and P.L. Lions, Hamilton-Jacobi equations with state constraints. Trans. Am. Math. Soc. 318 (1990) 643–683. [CrossRef] [MathSciNet]
- R. Courant and D. Hilbert, Methods of mathematical physics Vol. II. John Wiley & Sons (1989).
- M.G. Crandall, H. Ishii and P.L. Lions, User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1–67. [CrossRef] [MathSciNet]
- M. Garavello and P. Soravia, Optimality principles and uniqueness for Bellman equations of unbounded control problems with discontinuous running cost. Nonlin. Diff. Equations Appl. 11 (2004) 271–298. [CrossRef] [MathSciNet]
- G.W. Haynes and H. Hermes, Nonlinear controllability via Lie theory. SIAM J. Control 8 (1970) 450–460. [CrossRef] [MathSciNet]
- H. Ishii, A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations. Ann. Sc. Norm. Sup. Pisa (IV) 16 (1989) 105–135.
- M.A. Katsoulakis, Viscosity solutions of second order fully nonlinear elliptic equations with state constraints. Indiana Univ. Math. J. 43 (1994) 493–519. [CrossRef] [MathSciNet]
- P.L. Lions, Generalized solutions of Hamilton-Jacobi equations. Pitman (1982).
- R.T. Newcomb II and J. Su, Eikonal equations with discontinuities. Diff. Integral Equations 8 (1995) 1947–1960.
- D.N. Ostrov, Extending viscosity solutions to eikonal equations with discontinuous spatial dependence. Nonlinear Anal. TMA 42 (2000) 709–736. [CrossRef]
- F. Rampazzo and H. Sussmann, Set-valued differentials and a nonsmooth version of Chow's theorem, in Proc. of the 40th IEEE Conference on Decision and Control. Orlando, Florida (2001) 2613–2618.
- H.M. Soner, Optimal control problems with state constraints I. SIAM J. Control Optim. 24 (1987) 551–561.
- P. Soravia, Hölder continuity of the minimum time function with C1-manifold targets. J. Optim. Theory Appl. 75 (1992) 401–421. [CrossRef] [MathSciNet]
- P. Soravia, Discontinuous viscosity solutions to Dirichlet problems for Hamilton-Jacobi equations with convex hamiltonians. Commun. Partial Diff. Equations 18 (1993) 1493–1514. [CrossRef] [MathSciNet]
- P. Soravia, Boundary value problems for Hamilton-Jacobi equations with discontinuous Lagrangian. Indiana Univ. Math. J. 51 (2002) 451–476. [MathSciNet]
- P. Soravia, Uniqueness results for viscosity solutions of fully nonlinear, degenerate elliptic equations with discontinuous coefficients. Commun. Pure Appl. Anal. (To appear).
- A. Swiech, -interior estimates for solutions of fully nonlinear, uniformly elliptic equations. Adv. Differ. Equ. 2 (1997) 1005–1027.
- A. Tourin, A comparison theorem for a piecewise Lipschitz continuous Hamiltonian and applications to shape-from-shading. Numer. Math. 62 (1992) 75–85. [CrossRef] [MathSciNet]
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