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Solvability of the Riemann boundary-value problem on a fractal arc

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References

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

    Google Scholar 

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

    Google Scholar 

  3. A. A. Babaev and V. V. Salaev, “Boundary-value problems and singular equations on a rectifiable contour,” Mat. Zametki,31, No. 4, 571–580 (1982).

    Google Scholar 

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

    Google Scholar 

  5. E. A. Danilov, “The 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).

    Google Scholar 

  6. S. A. Plaksa, “The Riemann boundary-value problem with an oscillating coefficient and singular integral equations on a rectifiable curve,” Ukr. Mat. Zh.,41, No. 1, 116–121 (1989).

    Google Scholar 

  7. B. A. Kats, “A boundary-value problem on a nonsmooth contour of infinite length,” Mat. Zametki,33, No. 5, 669–678 (1983).

    Google Scholar 

  8. T. A. Zapuskalova, “The Riemann boundary-value problem on a spiral-shaped contour of infinite length,” in: Proceedings of Seminars on Boundary-Value Problems [in Russian], Kazan (1982), pp. 79–85.

  9. B. A. Kats, “The Riemann boundary-value problem on a nonrectifiable Jordan curve,” Dokl. Akad. Nauk SSSR,267, No. 4, 789–792 (1982).

    Google Scholar 

  10. B. A. Kats, “The Riemann problem on a closed Jordan curve,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 68–80 (1983).

    Google Scholar 

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

    Google Scholar 

  12. A. N. Kolmogorov and V. M. Tikhomirov, “ɛ-entropy andɛ-capacity of sets in function spaces,” Usp. Mat. Nauk,14, No. 2, 3–86 (1959).

    Google Scholar 

  13. B. B. Mandelbrot, Fractals: Form, Chance, and Dimension, W. H. Freeman and Co., San Francisco, Calif. (1977).

    Google Scholar 

  14. J. Feder, Fractals, Plenum Press, New York-London (1988).

    Google Scholar 

  15. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, New Jersey (1971).

    Google Scholar 

  16. I. N. Vekua, Generalized Analytic Functions [in Russian], Gos. Izd. Fiz.-Mat. Lit., Moscow (1959).

    Google Scholar 

  17. L. V. Hörmander, The Analysis of Linear Partial Differential Operators, Springer-Verlag, Berlin-New York (1983).

    Google Scholar 

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Translated from Matematicheskie Zametki, Vol. 53, No. 5, pp. 69–75, May, 1993.

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Kats, B.A. Solvability of the Riemann boundary-value problem on a fractal arc. Math Notes 53, 502–505 (1993). https://doi.org/10.1007/BF01208545

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