| Title:
|
Semipermeable surfaces for non-smooth differential inclusions (English) |
| Author:
|
Leśniewski, Andrzej |
| Author:
|
Rzeżuchowski, Tadeusz |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
131 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
261-278 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
differential inclusions |
| Keyword:
|
semipermeable surfaces |
| Keyword:
|
barrier solutions |
| MSC:
|
34A60 |
| MSC:
|
49J52 |
| MSC:
|
49N60 |
| idZBL:
|
Zbl 1115.34014 |
| idMR:
|
MR2248594 |
| DOI:
|
10.21136/MB.2006.134141 |
| . |
| Date available:
|
2009-09-24T22:26:19Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134141 |
| . |
| Reference:
|
[1] J.-P. Aubin: Viability Theory.Birkhauser, Boston, 1991. Zbl 0755.93003, MR 1134779 |
| Reference:
|
[2] J.-P. Aubin, H. Frankowska: Set-Valued Analysis.Birkhauser, Boston, 1990. MR 1048347 |
| Reference:
|
[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. MR 1466920, 10.1137/S0363012995287295 |
| Reference:
|
[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. MR 1466921, 10.1137/S0363012996312155 |
| Reference:
|
[5] H. Frankowska: Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equation.SIAM J. Control Optim. 31 (1993), 257–272. MR 1200233, 10.1137/0331016 |
| Reference:
|
[6] H. Frankowska, S. Plaskacz, T. Rze.zuchowski: Measurable viability theorems and the Hamilton-Jacobi-Bellman equation.J. Differ. Equations 116 (1995), 265–305. MR 1318576, 10.1006/jdeq.1995.1036 |
| Reference:
|
[7] R. Isaacs: Differential Games.John Wiley, New York, 1965. Zbl 0125.38001, MR 0210469 |
| Reference:
|
[8] J. Jarník, J. Kurzweil: On conditions for right-hand sides of differential relations.Čas. pěst. mat. 102 (1977), 334–349. MR 0466702 |
| Reference:
|
[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 0504159 |
| Reference:
|
[10] J. Jarník, J. Kurzweil: Sets of solutions of differential relations.Czechoslovak Math. J. 31 (1981), 554–568. MR 0631602 |
| Reference:
|
[11] J. Jarník, J. Kurzweil: Integral of multivalued mappings and its connection with differential relations.Čas. pěst. mat. 108 (1983), 8–28. MR 0694137 |
| Reference:
|
[12] P. Krbec, J. Kurzweil: Kneser’s theorem for multivalued differential delay equations.Čas. pěst. mat. 104 (1979), 1–8. MR 0523570 |
| Reference:
|
[13] A. Leśniewski, T. Rze.zuchowski: Autonomous differential inclusions sharing the families of trajectories.Accepted at Demonstratio Mathematica. |
| Reference:
|
[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. MR 1940532, 10.12775/TMNA.2002.027 |
| Reference:
|
[15] K. Przeslawski: Continuous Selectors. Part I: Linear Selectors.J. Convex Anal. 5 (1998), 249–267. MR 1670348 |
| Reference:
|
[16] M. Quincampoix: Differential inclusions and target problems.SIAM J. Control Optim. 30 (1992), 324–335. Zbl 0862.49006, MR 1149071, 10.1137/0330020 |
| Reference:
|
[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. Zbl 0459.28007, MR 0616201 |
| Reference:
|
[18] T. Rze.zuchowski: Boudary solutions of differential inclusions and recovering the initial data.Set-Valued Analysis 5 (1997), 181–193. MR 1463930, 10.1023/A:1008682614694 |
| Reference:
|
[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 0680625 |
| Reference:
|
[20] R. Schneider: Convex Bodies: The Brunn-Minkowski Theory.Cambridge University Press, Cambridge, 1993. Zbl 0798.52001, MR 1216521 |
| Reference:
|
[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 0028385 |
| Reference:
|
[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 0047123 |
| Reference:
|
[23] G. V. Smirnov: Introduction to the Theory of Differential Inclusions.American Mathematical Society, Providence, Rhode Island, 2002. Zbl 0992.34001, MR 1867542 |
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