IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i20p4360-d1263826.html
   My bibliography  Save this article

On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk

Author

Listed:
  • Astamur Bagapsh

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 40 Vavilova St., Moscow 119333, Russia
    Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow 119991, Russia)

  • Alexandre Soldatov

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 40 Vavilova St., Moscow 119333, Russia
    Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow 119991, Russia
    Department of Hiah Mathematics, Moscow Power Engineering Institute, National Research University, 14 Krasnokazarmennaya St., Moscow 111250, Russia)

Abstract

The role played by explicit formulas for solving boundary value problems for elliptic equations and systems is well known. In this paper, explicit formulas for a general solution of the Dirichlet problem for second-order elliptic systems in the unit disk are given. In addition, an iterative method for solving this problem for systems with respect to two unknown functions is described, and an integral representation of the Poisson type is obtained by applying this method.

Suggested Citation

  • Astamur Bagapsh & Alexandre Soldatov, 2023. "On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk," Mathematics, MDPI, vol. 11(20), pages 1-9, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4360-:d:1263826
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/20/4360/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/20/4360/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4360-:d:1263826. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.