Skip to main content
SpringerLink
Log in

On the Solution of the Exterior Dirichlet Problem for an Axisymmetric Potential

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

For an unbounded domain of the meridian plane with bounded smooth boundary that satisfies certain additional conditions, we develop a method for the reduction of the Dirichlet problem for an axisymmetric potential to Fredholm integral equations. In the case where the boundary of the domain is a unit circle, we obtain a solution of the exterior Dirichlet problem in explicit form.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. S. A. Plaksa, “Dirichlet problem for an axisymmetric potential in a simply-connected domain of the meridian plane,” Ukr. Mat. Zh., 53, No. 12, 1623–1640 (2001).

    Google Scholar 

  2. S. A. Plaksa, “On integral representations of an axisymmetric potential and the Stokes flow function in domains of the meridian plane. I,” Ukr. Mat. Zh., 53, No. 5, 631–646 (2001).

    Google Scholar 

  3. I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], Gostekhizdat, Moscow (1950).

    Google Scholar 

  4. N. Radzhabov, “Construction of potentials and investigation of interior and exterior boundary-value problems of the Dirichlet and Neumann types for the Euler - Poisson - Darboux equations on a plane,” Dokl. Akad. Nauk Tadzh. SSR, 17, No. 8, 7–11 (1974).

    Google Scholar 

  5. I. P. Mel'nichenko and S. A. Plaksa, “Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. II,” Ukr. Mat. Zh., 48, No. 12, 1695–1703 (1996).

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    S. A. Plaksa

Authors
  1. S. A. Plaksa
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Plaksa, S.A. On the Solution of the Exterior Dirichlet Problem for an Axisymmetric Potential. Ukrainian Mathematical Journal 54, 1982–1991 (2002). https://doi.org/10.1023/A:1024073231378

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1024073231378

Keywords

Search

Navigation