Geodesic
Properties of the solution of evolution inclusions driven by time dependent subdifferentials
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 2, pp. 197-204 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we consider evolution inclusions driven by a time-dependent sub\-differential. First we prove a relaxation result and then we use it to show that if the solution set is closed in a space of continuous functions, then the orientor field is almost everywhere convex valued.
In this paper we consider evolution inclusions driven by a time-dependent sub\-differential. First we prove a relaxation result and then we use it to show that if the solution set is closed in a space of continuous functions, then the orientor field is almost everywhere convex valued.
Classification : 34A60, 34G20, 49J24, 49J52
Keywords: subdifferential; monotonicity; relaxation; continuous selection; lower semicontinuous multifunction 
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Papageorgiou, Nikolaos S. Properties of the solution of evolution inclusions driven by time dependent subdifferentials. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 2, pp. 197-204. http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a1/

[1] Artstein Z., Prikry K.: Carathédory selections and the Scorza-Dragoni property. J. Math. Anal. Appl. 127 (1987), 540-547. | MR

[2] Aubin J.-P., Cellina A.: Differential Inclusions. Springer, Berlin, 1984. | MR | Zbl

[3] Barbu V.: Nonlinear Semigroups and Differential Equations in Banach Spaces. Noordhoff International Publishing, Leyden, The Netherlands, 1976. | MR | Zbl

[4] Brezis H.: Operateurs Maximaux Monotones. North Holland, Amsterdam, 1973. | Zbl

[5] Cellina A., Ornelas A.: Convexity and the closure of the solution set to differential inclusions. SISSA, Report No. 136M, Trieste, Italy, 1988. | Zbl

[6] Diestel J., Uhl J.J.: Vector Measures. Math. Surveys, Vol. 15, AMS, Providence, R.I., 1977. | MR | Zbl

[7] Klein E., Thompson A.: Theory of Correspondences. Wiley, New York, 1984. | MR | Zbl

[8] Papageorgiou N.S.: Measurable multifunctions and their applications to convex integral functionals. Intern. J. Math. and Math. Sci. 12 (1989), 175-192. | MR | Zbl

[9] Papageorgiou N.S.: On measurable multifunctions with applications to random multivalued equations. Math. Japonica 32 (1987), 437-464. | MR | Zbl

[10] Papageorgiou N.S.: On evolution inclusions associated with time dependent convex subdifferentials. Comment. Math. Univ. Carolinae 31 (1990), 517-527. | MR | Zbl

[11] Tsukada M.: Convergence of best approximations in smooth Banach spaces. J. Approx. Theory 40 (1984), 301-309. | MR

[12] Wagner D.: Survey of measurable selection theorems. SIAM J. Control and Optim. 15 (1977), 859-903. | MR | Zbl

[13] Watanabe J.: On certain nonlinear evolution equations. J. Math. Soc. Japan 25 (1973), 446-463. | MR | Zbl

[14] Yotsutani S.: Evolution equations associated with subdifferentials. J. Math. Soc. Japan 31 (1978), 623-646. | MR

[15] Jarnik J., Kurzweil J.: On conditions on right hand sides of differential relations. Časopis pro pěstování matematiky 102 (1977), 334-349. | MR | Zbl

[16] Rzezuchowski T.: Scorza-Dragoni type theorem for upper semicontinuous multivalued functions. Bulletin Polish Academy of Sciences 28 (1980), 61-66. | MR | Zbl