Skip to main content
Log in

A Generalization of the Neumann Problem for the Helmholtz Equation Outside Cuts on the Plane

  • Partial Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

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.

Institutional subscriptions

REFERENCES

  1. Krutitskii, P.A., Appl. Math. Letters, 2000, vol. 13, pp. 71–76.

    MATH  MathSciNet  Google Scholar 

  2. Lifanov, I.K., Metod singulyarnykh integral'nykh uravnenii i chislennyi eksperiment v matematicheskoi fizike, aerodinamike, teorii uprugosti i difraktsii voln (The Method of Singular Integral Equations and Numerical Experiment in Mathematical Physics, Aerodynamics, Elasticity, and Wave Diffraction), Moscow: Yanus, 1995.

    Google Scholar 

  3. Krutitskii, P.A., Zh. Vychislit. Mat. Mat. Fiz., 1994, vol. 34, no.8–9, pp. 1237–1257.

    MATH  MathSciNet  Google Scholar 

  4. Krutitskii, P.A., Zh. Vychislit. Mat. Mat. Fiz., 1994, vol. 34, no.11, pp. 1652–1665.

    MATH  MathSciNet  Google Scholar 

  5. Colton, D. and Kress, R., Integral Equation Methods in Scattering Theory, New York: Wiley, 1983. Translated under the title Metody integral'nykh uravnenii v teorii rasseyaniya, Moscow: Mir, 1987.

    Google Scholar 

  6. Krutitskii, P.A., Ann. Univ. Ferrara, 2001, vol. 47, pp. 285–296.

    MATH  MathSciNet  Google Scholar 

  7. Samarskii, A.A. and Andreev, V.B., Raznostnye metody dlya ellipticheskikh uravnenii (Difference Methods for Elliptic Equations), Moscow: Nauka, 1976.

    Google Scholar 

  8. Friedman, A. and Vogelius, M., Indiana Univ. Math. J., 1989, vol. 38, pp. 497–525.

    MathSciNet  Google Scholar 

  9. Muskhelishvili, N.I., Singulyarnye integral'nye uravneniya (Singular Integral Equations), Moscow, 1968.

  10. Vladimirov, V.S., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow, 1981.

  11. Smirnov, V.I., Kurs vysshei matematiki (Course of Higher Mathematics), Moscow, 1951, vol. 4.

  12. Nikiforov, A.F. and Uvarov, V.B., Spetsial'nye funktsii matematicheskoi fiziki (Special Functions of Mathematical Physics), Moscow, 1984.

  13. Krutitskii, P.A., Math. Meth. Appl. Sci., 1995, vol. 18, pp. 897–925.

    Article  MATH  MathSciNet  Google Scholar 

  14. Kolmogorov, A.N. and Fomin, S.V., Elementy teorii funktsii i funktsional'nogo analiza (Elements of Function Theory and Functional Analysis), Moscow, 1981.

  15. Matematicheskaya entsiklopediya (Mathematical Encyclopedia), Moscow, 1977, vol. 1, p. 915.

  16. Funktsional'nyi analiz (Functional Analysis), Krein, S.G., Ed., Moscow, 1964.

  17. Kantorovich, A.V. and Akilov, G.P., Funktsional'nyi analiz (Functional Analysis), Moscow, 1984.

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Differentsial'nye Uravneniya, Vol. 41, No. 9, 2005, pp. 1155–1165.

Original Russian Text Copyright © 2005 by Krutitskii, Kolybasova.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krutitskii, P.A., Kolybasova, V.V. A Generalization of the Neumann Problem for the Helmholtz Equation Outside Cuts on the Plane. Diff Equat 41, 1213–1224 (2005). https://doi.org/10.1007/s10625-005-0271-6

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10625-005-0271-6

Keywords

Navigation