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Abstrakty
The problem of existence of adjoint functions to boundary solutions is considered – it depends on the geometry of the attained set at the end point. This is applied to prove the smoothness of boundary solutions in the case of strictly convex right-hand side of di.erential inclusion which in turn permitts to show the smoothness of barrier solutions on semipermeable surfaces.
Wydawca
Czasopismo
Rocznik
Tom
Strony
107--114
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- Faculty of Mathematics & Information Science Warsaw University of Technology Plac Politechniki 1 00-661 Warsaw, Poland
Bibliografia
- [1] J.-P. Aubin, H. Frankowska, Set-Valued Analysis, Birkhauser, Boston, 1990. Zbl 0713.49021.
- [2] P. Cardaliaguet, On the regularity of semipereable surfaces in control theory with application to the optimal exit-time problem (Part I), SIAM J. Control Optim. 35 (1997), 1638–1652. Zbl 0889.49002.
- [3] P. Cardaliaguet, On the regularity of semipereable surfaces in control theory with application to the optimal exit-time problem (Part II), SIAM J. Control Optim. 35 (1997), 1653–1671. Zbl 0889.49003.
- [4] F. Clarke, Optimization and Nonsmooth Analysis, John Wiley, New York, 1983. Zbl 0696.49002.
- [5] F. Clarke, Yu. Ledyaev, R. Stern, P.Wolenski, Nonsmooth Analysis and Control Theory, Springer, New York, 1998. Zbl 1047.49500.
- [6] R. Isaacs, Differential Games, John Wiley, New York, 1965. Zbl 0125.38001.
- [7] I. Ekeland, M. Valadier, Representations of set-valued mappings, J. Math. Anal. & Appl. ] 35 (1971), 621-629. Zbl 0246.54018.
- [8] E. Lee, L. Markus, Foundations of optimal control theory, Wiley, New York, 1967. Zbl 0159.13201.
- [9] A. Leśniewski, T. Rzeżuchowski, Autonomous differential inclusions sharing the families of trajectories, Demonstratio Math. 39 (2) (2006), 347–356.
- [10] A. Leśniewski, T. Rzeżuchowski, Semipermeable surfaces for non-smooth differential inclusions, Mathematica Bohemica No 3 (2006), 261–278.
- [11] A. Ornelas, Parametrization of Carathéodory multifunctions, Rend. Sem. Mat. Univ. Padova 83 (1990), 33–44. Zbl 0708.28005.
- [12] L. Pontriagin, V. Boltyanski, V. Gamkrelidze, E. Mischenko, The Mathematical Theory of Optimal Processes, Wiley, New York, 1962. Zbl 0516.49001.
- [13] M. Quincampoix, Differential inclusions and target problems, SIAM J. Control Optim. 30 (1992), 324–335. Zbl 0862.49006.
- [14] R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge University Press, Cambridge, 1993. Zbl 0798.52001.
- [15] G. V. Smirnov, Introduction to the Theory of Differential Inclusions, American Mathematical Society, Providence, Rhode Island, Graduate Studies in Mathematics, volume 41, 2002. Zbl 0992.34001.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0033-0012