Geodesic
Jump boundary-value problem on a contour with elongate singularities
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2017), pp. 12-16.

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

Let $\Gamma$ be an image of the interval $(0,1)$ under one-to-one continuous mapping $\phi: (0,1)\to \mathbb{C}$. If the difference of closure of $\Gamma$ and the very set $\Gamma$ contains more than one point, then we say that $\Gamma$ is a contour with elongate singularities. We study the jump boundary-value problem for analytical functions on that contours and obtain new solvability criteria for it.
Keywords: jump problem, contour with singularities. 
@article{IVM_2017_1_a1,
     author = {B. A. Kats and S. R. Mironova and A. Yu. Pogodina},
     title = {Jump boundary-value problem on a contour with elongate singularities},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {12--16},
     publisher = {mathdoc},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_1_a1/}
}
TY  - JOUR
AU  - B. A. Kats
AU  - S. R. Mironova
AU  - A. Yu. Pogodina
TI  - Jump boundary-value problem on a contour with elongate singularities
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 12
EP  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_1_a1/
LA  - ru
ID  - IVM_2017_1_a1
ER  - 
%0 Journal Article
%A B. A. Kats
%A S. R. Mironova
%A A. Yu. Pogodina
%T Jump boundary-value problem on a contour with elongate singularities
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 12-16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_1_a1/
%G ru
%F IVM_2017_1_a1
B. A. Kats; S. R. Mironova; A. Yu. Pogodina. Jump boundary-value problem on a contour with elongate singularities. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2017), pp. 12-16. http://geodesic.mathdoc.fr/item/IVM_2017_1_a1/

[1] Gakhov F. D., Kraevye zadachi, Nauka, M., 1977

[2] Muskhelishvili H. I., Singulyarnye integralnye uravneniya, Nauka, M., 1962

[3] Kats B. A., “O kraevoi zadache Rimana so stepennym sdvigom”, Izv. vuzov. Matem., 1987, no. 8, 18–26 | MR

[4] Kats B. A., Mironova S. R., Pogodina A. Yu., “Zadacha o skachke na konture s predelnym kontinuumom”, Izv. vuzov. Matem., 2015, no. 2, 70–75

[5] Kats B. A., “Kraevaya zadacha Rimana na nespryamlyaemoi zhordanovoi krivoi”, DAN SSSR, 267:4 (1982), 789–792 | MR | Zbl

[6] Kats B. A., “Zadacha Rimana na razomknutoi zhordanovoi krivoi”, Izv. vuzov. Matem., 1983, no. 12, 30–38

[7] Kats B. A., “The Riemann boundary value problem on non-rectifiable curves and related questions”, Complex Var. Elliptic Equ., 59:8 (2014), 1053–1069 | DOI | MR | Zbl

[8] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973

[9] Vekua I. N., Obobschennye analiticheskie fuktsii, Nauka, M., 1988 | MR

[10] Falconer K. J., Fractal geometry, 3rd ed., Wiley and Sons, 2014 | MR | Zbl

[11] Kolmogorov A. N., Tikhomirov V. M., “$\varepsilon$-entropiya i emkost mnozhestv v funktsionalnykh prostranstvakh”, UMN, 14:2 (1959), 3–86 | Zbl

[12] Rainlevé P., Sur les lignes singulières des fonctions analytiques, These, Gauthier-Villars, Paris, 1887