Geodesic
The Riemann boundary value problem on a nonsmooth open curve
Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 135-148 
R. K. Seifullaev. The Riemann boundary value problem on a nonsmooth open curve. Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 135-148. http://geodesic.mathdoc.fr/item/SM_1981_40_2_a0/
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     title = {The {Riemann} boundary value problem on a~nonsmooth open curve},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to the study of the Riemann boundary value problem on an open curve. It is revealed that in some cases the solution of this problem differs in a fundamental way from all extant results in this area. Classes of curves (spirals) are singled out on which it is possible to comprehend the essence of the phenomenon under investigation, and a complete solution of the Riemann boundary value problem is found for these classes. Bibliography: 9 titles.

[1] A. A. Babaev, V. V. Salaev, “Odnomernyi singulyarnyi operator s nepreryvnoi plotnostyu po zamknutoi krivoi”, DAN SSSR, 209:6 (1973), 1257–1260 | MR | Zbl

[2] S. K. Balashov, “Ob osobom integrale Koshi po spiralyam”, Izv. AN BSSR, seriya fiz.-matem. nauk, 1973, no. 2, 43–51 | Zbl

[3] F. D. Gakhov, Kraevye zadachi, izd-vo “Nauka”, Moskva, 1977 | MR | Zbl

[4] N. I. Muskhelishvili, Singulyarnye integralnye uravneniya, izd-vo “Nauka”, Moskva, 1968 | MR

[5] B. Riman, Sochineniya, Gostekhizdat, Moskva–Leningrad, 1948

[6] V. V. Salaev, “Pryamye i obratnye otsenki dlya osobogo integrala Koshi po zamknutoi krivoi”, Matem. zametki, 19:3 (1976), 365–380 | MR | Zbl

[7] R. K. Seifullaev, Kraevaya zadacha Rimana na negladkoi razomknutoi krivoi, Dep. VINITI, No 3455-78, 1978 | MR

[8] R. K. Seifullaev, “Integral tipa Koshi po razomknutoi krivoi i zadacha skachka”, Uchenye zapiski MB i SSO Azerb.SSR, seriya fiz.-matem. nauk, 1977, no. 4, 45–52

[9] G. A. Khuskivadze, “Ob osobom integrale i integrale tipa Koshi”, Trudy Tbilisk. matem. in-ta AN Gruz.SSR, 53:7 (1976), 73–86 | Zbl