On the weak polar cone of the solution set of a differential inclusion with conic graph
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 238-246 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A differential inclusion with values in a reflexive Banach space such that its right-hand side is at each time a convex closed cone is considered. The form of the weak polar cone of the cone of strongly bounded solutions to the Cauchy problem for this inclusion is found. A solution is called strongly bounded if it is an absolutely continuous function (in a wide sense) and its derivative is essentially bounded.
Keywords: polar cone, multivalued mapping, differential inclusion, convex process.
@article{TIMM_2014_20_4_a20,
     author = {E. S. Polovinkin},
     title = {On the weak polar cone of the solution set of a~differential inclusion with conic graph},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {238--246},
     year = {2014},
     volume = {20},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a20/}
}
TY  - JOUR
AU  - E. S. Polovinkin
TI  - On the weak polar cone of the solution set of a differential inclusion with conic graph
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2014
SP  - 238
EP  - 246
VL  - 20
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a20/
LA  - ru
ID  - TIMM_2014_20_4_a20
ER  - 
%0 Journal Article
%A E. S. Polovinkin
%T On the weak polar cone of the solution set of a differential inclusion with conic graph
%J Trudy Instituta matematiki i mehaniki
%D 2014
%P 238-246
%V 20
%N 4
%U http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a20/
%G ru
%F TIMM_2014_20_4_a20
E. S. Polovinkin. On the weak polar cone of the solution set of a differential inclusion with conic graph. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 238-246. http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a20/

[1] Aubin J.-P., Frankowska H., Set-valued analysis, Birkhäuser, Boston, 1990, 461 pp. | MR | Zbl

[2] Diestel J., “Remarks on weak compactness in $L_1(\mu,X)$”, Glasgow Math. J., 18:1 (1977), 87–91 | DOI | MR | Zbl

[3] Dunford N., Pettis B. J., “Linear operators on summable functions”, Trans. Amer. Math. Soc., 47 (1940), 323–392 | DOI | MR | Zbl | Zbl

[4] Danford N., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, IL, M., 1962; УРСС, М., 2004, 896 с.

[5] Ioffe A. D., Tikhomirov V. M., Teoriya ekstremalnykh zadach, Nauka, M., 1974, 480 pp. | MR | Zbl

[6] Polovinkin E. S., “O vychislenii polyarnogo konusa ko mnozhestvu reshenii differentsialnogo vklyucheniya”, Tr. MIAN, 278, 2012, 178–187 | MR | Zbl

[7] Polovinkin E. S., Balashov M. V., Elementy vypuklogo i silno vypuklogo analiza, 2-e izd., Fizmatlit, M., 2007, 440 pp. | Zbl

[8] Rudin U., Osnovy matematicheskogo analiza, Mir, M., 1976, 320 pp.

[9] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970, 720 pp. | MR

[10] Edvards R., Funktsionalnyi analiz. Teoriya i prilozheniya, Mir, M., 1969, 1072 pp.