Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We prove an existence and uniqueness result for the solutions to the Skorokhod problem on uniformly prox-regular sets through a deterministic approach. This result can be applied in order to investigate some regularity properties of the value function for differential games with reflection on the boundary.
Czasopismo
Rocznik
Tom
Strony
787--802
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- SISSA/ISAS, via Beirut, 2-4 - 34013 Trieste, Italy, bettiol@sissa.it
Bibliografia
- AUBIN, J.-P. and FRANKOWSKA, H. (1990) Set-valued analysis. Systems & Control: Foundations & Applications 2. Birkhäuser Boston, Basel, Berlin.
- BARDI, M. and CAPUZZO-DOLCETTA, I. (1997) Optimal control and viscosity solutions of the Hamilton-Jacobi equations. Birkhäuser, Boston.
- BARLES, G. (1994) Solutions de viscosité des équations de Hamilton-Jacobi. (French) [Viscosity solutions of Hamilton-Jacobi equations] . Mathématiques & Applications [Mathematics & Applications], 17, Springer-Verlag, Paris.
- BETTIOL, P. (2002) Weak Solutions in Hamilton-Jacobi and Control Theory. PhD Thesis.
- BETTIOL, P. (2005) On ergodic problem for Hamilton-Jacobi-Isaacs equations. ESAIM COCV 11, 522-541.
- CLARKE, F.H., STERN, R.J. and WOLENSKI, P.R. (1995) Proximal smoothness and the lower-C2 property. J. Convex Analysis 2, 117-144.
- CORNET, B. (1983) Existence of slow solutions for a class of differential inclusions. J. Math. Anal. Appl. 96, 130-147.
- DELFOUR, M.C. and ZOLESIO, J.P. (1994) Shape analysis via oriented distance functions. J. Fund. Anal. 123 (1), 129-201.
- DELFOUR, M.C. and ZOLESIO, J.P. (2004) Oriented distance function and its evolution equation for initial sets with thin boundary. SIAM J. Control Optim. 42 (6), 2286-2304.
- FEDERER, H. (1959) Curvature measures. Trans. Amer. Math. Soc. 93, 418-491.
- FRANKOWSKA, H. (1985) A viability approach to the Skorohod problem. Stochastics 14 (3), 227-244.
- FRANKOWSKA, H. and PLASKACZ, S. (1996) A measurable upper semicontinuous viability theorem for tubes. Nonlinear Analysis JMA 26, 565-582.
- HENRY, C. (1973) An existence theorem for a class of differential equations with multivalued right-hand side. J. Math Anal. Appl. 41, 179-186.
- ISHII, H. (1988) Lecture Notes on Viscosity Solutions. Brown University, Providence, RI.
- LIONS, P.L. (1982) Generalized solutions of Hamilton-Jacobi equations. Research Notes in Mathematics 69. Pitman (Advanced Publishing Program), Boston, London.
- LIONS, P.L. (1985) Neumann type boundary conditions for Hamilton-Jacobi equations. Duke Math. J. 52 (4), 793-820.
- LIONS, P.L. and SZNITMAN, A.S. (1984) Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math. 37 (4), 511-537.
- ROCKAFELLAR, R.T. and WETS, R.J.-B. (1998) Variational analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 317, Springer-Verlag, Berlin.
- POLIQUIN, R.A., ROCKAPELLAR, R.T. and THIBAULT, L. (2000) Local differentiability of distance functions. Trans. Amer. Math. Soc. 352(11), 5231-5249.
- SEREA, O.-S. (2003) On reflecting boundary problem for optimal control. SIAM J. Control Optim. 42 (2), 559-575.
- THIBAULT, L. (2003) Sweeping process with regular and nonregular sets. J. Differential Equation 193, 1-26.
- VINTER, R.B. (2000) Optimal Control. Birkhäuser, Boston, Basel, Berlin.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0014-0020