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Warianty tytułu
Języki publikacji
Abstrakty
The exterior sphere condition is compared to proximal smoothness, and examples are provided, which show that the two properties are not necessarily equivalent. Then conditions are given under which equivalence holds, and an open question involving the union of uniform closed balls property is stated in the form of a conjecture.
Czasopismo
Rocznik
Tom
Strony
1525--1534
Opis fizyczny
Bibliogr. 20 poz., rys.
Twórcy
autor
autor
autor
- Department of Computer Science and Mathematics, Lebanese American University, Byblos Campus, P.O. Box 36, Byblos, Lebanon, cnour@lau.edu.lb
Bibliografia
- ALVAREZ, O., CARDALIAGUET, P. and MONNEAU, R. (2005) Existence and uniqueness for dislocation dynamics with positive velocity. Interfaces Free Bound. 7 (4), 415-434.
- CANINO, A. (1988) On p-convex sets and geodesies. J. Differential Equations 75 (1), 118-157.
- CANNARSA, P. and CARDALIAGUET, P. (2006) Perimeter estimates for reachable sets of control systems. J. Convex Anal. 13, 2, 253-267.
- CANNARSA, P. and FRANKOWSKA, H. (2006) Interior sphere property of attainable sets and time optimal control problems. ESAIM: Control Optim. Calc. Var. 12, 350-370.
- CANNARSA, P. and SINESTRARI, C. (1995) Convexity properties of the minimum time function. Calc. Var. 3, 273-298.
- CANNARSA, P. and SINESTRARI, C. (2004) Semiconcave Functions, Hamiton-Jacobi Equations and Optimal Control. Birkhäuser, Boston.
- CLARKE, F.H., LEDYAEV, Yu., STERN, R. and WOLENSKI, P. (1998) Non-smooth Analysis and Control Theory. Graduate Texts in Mathematics 178. Springer-Verlag, New York.
- CLARKE, F.H., STERN, R. and WOLENSKI, P. (1995) Proximal smoothness and the lower-C2 property. J. Convex Anal. 2, 117-144.
- COLOMBO, G. and MARIGONDA, A. (2005) Differentiability properties for a class of non-convex functions. Calc. Var. 25, 1-31.
- COLOMBO, G., MARIGONDA, A. and WOLENSKI, P. (2006) Some new regularity properties for the minimal time function. SIAM J. Control Optim. 44 (6), 2285-2299.
- FEDERER, H. (1959) Curvature measures. Trans. Amer. Math. Soc. 93, 418-491.
- GORNIEWICZ, L. (1995) Topological approach to differential inclusions. In: Topological Methods in Differential Equations and Inclusions. NATO Adv. Sci. Inst. (Series C Math. Phys.) 472, Kluwer Academic, Dordrecht, 129-190.
- MARIGONDA, A. (2006) Differentiability properties for a class of non-Lipschitz functions and applications. Ph.D. thesis, University of Padova, Italy.
- NOUR, C., STERN, R.J. and TAKCHE, J. (2009) Proximal smoothness and the exterior sphere condition. J. Convex Anal., to appear.
- POLIQUIN, R.A. and ROCKAFELLAR, R.T. (1996) Prox-regular functions in variational analysis. Trans. Amer. Math. Soc. 348, 1805-1838.
- POLIQUIN, R.A., ROCKAFELLAR, R.T. and THIBAULT, L. (2000) Local differentiability of distance functions. Trans. Amer. Math. Soc. 352, 5231-5249.
- ROCKAFELLAR, R.T. (1979) Clarke’s tangent cones and the boundaries of closed sets in Rn. Nonlinear Anal. Theor. Meth. Appl. 3, 145-154.
- ROCKAFELLAR, R.T. and WETS, R.J.B. (1998) Variational Analysis. Grundlehren der Mathematischen Wissenschaften 317. Springer-Verlag, Berlin.
- SHAPIRO, A.S. (1994) Existence and differentiability of metric projections in Hilbert spaces. SIAM J. Optim. 4, 231-259.
- SINESTRARI, C. (2004) Semiconcavity of the value function for exit time problems with nonsmooth target. Commun. Pure Appl. Anal. 3 (4), 757-774.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0046-0027