Geodesic
Semipermeable surfaces for non-smooth differential inclusions
Mathematica Bohemica, Tome 131 (2006) no. 3, pp. 261-278
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We investigate the regularity of semipermeable surfaces along barrier solutions without the assumption of smoothness of the right-hand side of the differential inclusion. We check what can be said if the assumptions concern not the right-hand side itself but the cones it generates. We examine also the properties of families of sets with semipermeable boundaries.
We investigate the regularity of semipermeable surfaces along barrier solutions without the assumption of smoothness of the right-hand side of the differential inclusion. We check what can be said if the assumptions concern not the right-hand side itself but the cones it generates. We examine also the properties of families of sets with semipermeable boundaries.
DOI : 10.21136/MB.2006.134141
Classification : 34A60, 49J52, 49N60
Keywords: differential inclusions; semipermeable surfaces; barrier solutions 
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Leśniewski, Andrzej; Rzeżuchowski, Tadeusz. Semipermeable surfaces for non-smooth differential inclusions. Mathematica Bohemica, Tome 131 (2006) no. 3, pp. 261-278. doi: 10.21136/MB.2006.134141

[1] J.-P. Aubin: Viability Theory. Birkhauser, Boston, 1991. | MR | Zbl

[2] J.-P. Aubin, H. Frankowska: Set-Valued Analysis. Birkhauser, Boston, 1990. | MR

[3] P. Cardaliaguet: On the regularity of semipermeable surfaces in control theory with application to the optimal exit-time problem (Part I). SIAM J. Control Optim. 35 (1997), 1638–1652. | DOI | MR

[4] P. Cardaliaguet: On the regularity of semipermeable surfaces in control theory with application to the optimal exit-time problem (Part II). SIAM J. Control Optim. 35 (1997), 1653–1671. | DOI | MR

[5] H. Frankowska: Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equation. SIAM J. Control Optim. 31 (1993), 257–272. | DOI | MR

[6] H. Frankowska, S. Plaskacz, T. Rze.zuchowski: Measurable viability theorems and the Hamilton-Jacobi-Bellman equation. J. Differ. Equations 116 (1995), 265–305. | DOI | MR

[7] R. Isaacs: Differential Games. John Wiley, New York, 1965. | MR | Zbl

[8] J. Jarník, J. Kurzweil: On conditions for right-hand sides of differential relations. Čas. pěst. mat. 102 (1977), 334–349. | MR

[9] J. Jarník, J. Kurzweil: Extension of a Scorza-Dragoni theorem to differential relations and functional-differential relations. Commentationes Mathematicae, Tomus specialis in honorem Ladislai Orlicz, I. Polish Scientific Publishers, Warsaw (1978), 147–158. | MR

[10] J. Jarník, J. Kurzweil: Sets of solutions of differential relations. Czechoslovak Math. J. 31 (1981), 554–568. | MR

[11] J. Jarník, J. Kurzweil: Integral of multivalued mappings and its connection with differential relations. Čas. pěst. mat. 108 (1983), 8–28. | MR

[12] P. Krbec, J. Kurzweil: Kneser’s theorem for multivalued differential delay equations. Čas. pěst. mat. 104 (1979), 1–8. | MR

[13] A. Leśniewski, T. Rze.zuchowski: Autonomous differential inclusions sharing the families of trajectories. Accepted at Demonstratio Mathematica.

[14] S. Plaskacz, M. Quincampoix: Representation formulas for Hamilton Jacobi equations related to calculus of variation problems. Topol. Methods Nonlin. Anal. 20 (2002), 85–118. | DOI | MR

[15] K. Przeslawski: Continuous Selectors. Part I: Linear Selectors. J. Convex Anal. 5 (1998), 249–267. | MR

[16] M. Quincampoix: Differential inclusions and target problems. SIAM J. Control Optim. 30 (1992), 324–335. | DOI | MR | Zbl

[17] T. Rze.zuchowski: Scorza-Dragoni type theorem for upper semicontinuous multivalued functions. Bull. Acad. Polon. Sc., Sér. Sc. Math. Phys. 28 (1980), 61–66. | MR | Zbl

[18] T. Rze.zuchowski: Boudary solutions of differential inclusions and recovering the initial data. Set-Valued Analysis 5 (1997), 181–193. | DOI | MR

[19] T. Rze.zuchowski: On the set where all the solutions satisfy a differential inclusion. Qualitative Theory of Differential Equations, Szeged, 1979, pp. 903–913. | MR

[20] R. Schneider: Convex Bodies: The Brunn-Minkowski Theory. Cambridge University Press, Cambridge, 1993. | MR | Zbl

[21] G. Scorza-Dragoni: Un theorema sulle funzioni continue rispetto ad una e misurabili rispetto ad un’altra variabile. Rendiconti Sem. Mat. Padova 17 (1948), 102–106. | MR

[22] G. Scorza-Dragoni: Una applicazione della quasi-continuità semiregolare delle funzioni misurabili rispetto ad una e continue rispetto ad un’altra variabile. Atti Acc. Naz. Lincei 12 (1952), 55–61. | MR

[23] G. V. Smirnov: Introduction to the Theory of Differential Inclusions. American Mathematical Society, Providence, Rhode Island, 2002. | MR | Zbl

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