Skip to main content
Log in

Riemann boundary-value problem on an open rectifiable jordan curve. I

  • Published:
Ukrainian Mathematical Journal Aims and scope

The Riemann boundary-value problem is solved for the classes of open rectifiable Jordan curves extended as compared with previous results and functions defined on these curves.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. F. D. Gakhov, Boundary-Value Problems [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  2. N. I. Muskhelishvili, Singular Integral Equations [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  3. R. K. Seifullaev, “Riemann boundary-value problem on a nonsmooth open curve,” Mat. Sb., 112, No. 2, 147–161 (1980).

    MathSciNet  Google Scholar 

  4. N. V. Govorov, Riemann Boundary-Value Problem with Infinite Index [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  5. B. A. Kats, “On the exclusive case of the Riemann problem with oscillating coefficient,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 12, 41–50 (1981).

  6. E. A. Danilov, “Dependence of the number of solutions of the homogeneous Riemann problem on the contour and the modulus of the coefficient,” Dokl. Akad. Nauk SSSR, 264, No. 6, 1305–1308 (1982).

    MathSciNet  Google Scholar 

  7. B. A. Kats, “Riemann problem on an open Jordan curve,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 12, 30–38 (1983).

  8. B. Gonzalez and J. Reyes, “The homogeneous Riemann boundary-value problem on rectifiable open Jordan curves,” Cience. Mat. Havana, 9, No. 2, 3–9 (1988).

    Google Scholar 

  9. S. A. Plaksa, “Riemann boundary-value problem with oscillating coefficient and singular integral equations on a rectifiable curve,” Ukr. Mat. Zh., 41, No. 1, 116–121 (1989); English translation: Ukr. Math. J., 41, No. 1, 107–112 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  10. B. A. Kats, “Riemann boundary-value problem on fractal arcs and arcs of infinite length. I,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 6, 7–16 (1993); English translation: Russian Math., 37, No. 6, 4–13 (1993).

  11. B. A. Kats, “Riemann boundary-value problem on fractal arcs and arcs of infinite length. II,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 7, 17–23 (1993); English translation: Russian Math., 37, No. 7, 15–21 (1993).

  12. K. Kutlu, “On Riemann boundary-value problem,” An. Univ. Timişoara. Ser. Mat.-Inform., 38, No. 1, 89–96 (2000).

    MathSciNet  MATH  Google Scholar 

  13. D. Pena and J. Reyes, “Riemann boundary value problem on a regular open curve,” J. Natur. Geom., 22, No. 1, 1–17 (2002).

    MATH  Google Scholar 

  14. Yu. V. Vasil’eva and S. A. Plaksa, “Piecewise-continuous Riemann boundary-value problem on a rectifiable curve,” Ukr. Mat. Zh., 58, No. 5, 616–628 (2006); English translation: Ukr. Math. J., 58, No. 5., 694–708 (2006).

    MathSciNet  MATH  Google Scholar 

  15. V. V. Salaev, “Direct and inverse estimates for a singular Cauchy integral along a closed curve,” Mat. Zametki, 19, No. 3, 365–380 (1976).

    MathSciNet  MATH  Google Scholar 

  16. S. A. Plaksa, “Riemann boundary-value problem with infinite index of logarithmic order on a spiral contour. I,” Ukr. Mat. Zh., 42, No. 11, 1509–1517 (1990); English translation: Ukr. Math. J., 42, No. 11, 1351–1358 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  17. O. F. Gerus, “Some estimates of smoothness moduli for the Cauchy-type integrals,” Ukr. Mat. Zh., 30, No. 5, 594–601 (1978); English translation: Ukr. Math. J., 30, No. 5, 445–460 (1978).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 11, pp. 1511–1522, November, 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Plaksa, S.A., Kud’yavina, Y... Riemann boundary-value problem on an open rectifiable jordan curve. I. Ukr Math J 62, 1752–1765 (2011). https://doi.org/10.1007/s11253-011-0465-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-011-0465-4

Keywords

Navigation