Geodesic
On a Counterexample in Analysis
Matematičeskie zametki, Tome 95 (2014) no. 1, pp. 123-128.

Voir la notice de l'article provenant de la source Math-Net.Ru

An example of multivalued convex-valued Lipschitz mapping from $\mathbb R^n$ into $\mathbb R^m$ such that, at any point, the support function of this mapping has no mixed derivatives in the sense of Gâteaux with respect to the initial and conjugate variables is constructed.
Keywords: multivalued convex-valued Lipschitz mapping, support function, convex analysis, Cantor function. 
@article{MZM_2014_95_1_a9,
     author = {E. S. Polovinkin},
     title = {On a {Counterexample} in {Analysis}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {123--128},
     publisher = {mathdoc},
     volume = {95},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a9/}
}
TY  - JOUR
AU  - E. S. Polovinkin
TI  - On a Counterexample in Analysis
JO  - Matematičeskie zametki
PY  - 2014
SP  - 123
EP  - 128
VL  - 95
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a9/
LA  - ru
ID  - MZM_2014_95_1_a9
ER  - 
%0 Journal Article
%A E. S. Polovinkin
%T On a Counterexample in Analysis
%J Matematičeskie zametki
%D 2014
%P 123-128
%V 95
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a9/
%G ru
%F MZM_2014_95_1_a9
E. S. Polovinkin. On a Counterexample in Analysis. Matematičeskie zametki, Tome 95 (2014) no. 1, pp. 123-128. http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a9/

[1] E. S. Polovinkin, Elementy teorii mnogoznachnykh otobrazhenii, Izd-vo MFTI, M., 1982

[2] E. S. Polovinkin, Teoriya mnogoznachnykh otobrazhenii, Izd-vo MFTI, M., 1983

[3] E. S. Polovinkin, “Silno vypuklyi analiz”, Matem. sb., 187:2 (1996), 103–130 | DOI | MR | Zbl

[4] I. M. Prudnikov, “Subdifferentsial Klarka dlya lipshitsevykh mnogoznachnykh otobrazhenii”, Kibernetika i sistemnyi analiz, 1992, no. 1, 176–180 | MR

[5] E. S. Polovinkin, M. V. Balashov, Elementy vypuklogo i silno vypuklogo analiza, Fizmatlit, M., 2007

[6] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976 | MR

[7] B. Gelbaum, Dzh. Olmsted, Kontrprimery v analize, Mir, M., 1967 | MR | Zbl