Differential Equations

, Volume 54, Issue 4, pp 486–496 | Cite as

Oblique Derivative Problem for the Helmholtz Equation in a Disk

  • A. A. Polosin
Partial Differential Equations


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


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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.zbMATHGoogle Scholar
  2. 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.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 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.zbMATHGoogle Scholar
  4. 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.zbMATHGoogle Scholar
  5. 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.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 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.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 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. 8.
    Prudnikov, A.P., Brychkov, Yu.A., and Marichev, O.I., Integraly i ryady. Elementarnye funktsii (Integrals and Series: Elementary Functions), Moscow: Nauka, 1981.zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

Personalised recommendations