Skip to main content
Log in

Oblique Derivative Problem for the Helmholtz Equation in a Disk

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

Abstract

We show that the oblique derivative problem for the Helmholtz equation in a disk is uniquely solvable under certain restrictions on the parameter.

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. Il’in, V.A. and Moiseev, E.I., The system of root functions of the directional derivative problem is not a basis, Differ. Equations, 1994, vol. 30, no. 1, pp. 119–132.

    MATH  Google Scholar 

  2. Polosin, A.A., Oblique derivative problem with variable inclination angle: Location of the spectrum and the absence of the basis property of the system of root functions, Differ. Equations, 2011, vol. 47, no. 10, pp. 1482–1489.

    Article  MathSciNet  MATH  Google Scholar 

  3. Moiseev, E.I., Location of the spectrum of a boundary value problem with mixed boundary conditions, Differ. Equations, 1988, vol. 24, no. 1, pp. 98–107.

    MATH  Google Scholar 

  4. Moiseev, E.I., Distribution of the spectrum of the Tricomi problem for the Lavrent’ev–Bitsadze equation, Differ. Equations, 1989, vol. 25, no. 1, pp. 77–84.

    MATH  Google Scholar 

  5. Polosin, A.A., On the location of the spectrum of a mixed boundary value problem in a square, Differ. Equations, 2002, vol. 38, no. 8, pp. 1166–1172.

    Article  MathSciNet  MATH  Google Scholar 

  6. Polosin, A.A., On the location of the spectrum of a mixed boundary value problem in a half-disk, Differ. Equations, 2006, vol. 42, no. 5, pp. 684–697.

    Article  MathSciNet  MATH  Google Scholar 

  7. Watson, G., A Treatise of the Theory of Bessel Functions, Cambridge: Cambridge Univ., 1945. Translated under the title Teoriya besselevykh funktsii, Moscow: Mir, 1949, Part1.

    Google Scholar 

  8. Prudnikov, A.P., Brychkov, Yu.A., and Marichev, O.I., Integraly i ryady. Elementarnye funktsii (Integrals and Series: Elementary Functions), Moscow: Nauka, 1981.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Polosin.

Additional information

Original Russian Text © A. A. Polosin, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 4, pp. 492–501.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Polosin, A.A. Oblique Derivative Problem for the Helmholtz Equation in a Disk. Diff Equat 54, 486–496 (2018). https://doi.org/10.1134/S0012266118040067

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266118040067

Navigation