IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-2002-2_13.html

Singularities

In: Computational Conformal Mapping

Author

Listed:
  • Prem K. Kythe

    (University of New Orleans, Department of Mathematics)

Abstract

As Radon (1919) and Carleman (1922) have shown, the method of integral equations can also be used to solve the problem of potential theory when the boundary Γ of a simply connected region D contains corners. In such cases Carleman separates the kernel into two parts, one of which corresponds to the corner singularities, whereas Radon uses the Stieltjes integral equations to solve this problem. We shall derive the analogues of Gershgorin’s integral equation and then obtain Arbenz’s integral equation which uses Radon’s method to determine conformal maps for boundaries with corners and has a unique solution. The cases of interior and exterior mapping functions f(z) and f E (z) are related to each other through inversion by the relations (7.3.12). We are interested in the behavior of these univalent maps and those of doubly connected regions at singularities on and near the boundary, which are corner-type or pole-type. The nature and location of such singularities are determined.

Suggested Citation

  • Prem K. Kythe, 1998. "Singularities," Springer Books, in: Computational Conformal Mapping, chapter 0, pages 320-357, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2002-2_13
    DOI: 10.1007/978-1-4612-2002-2_13
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:sprchp:978-1-4612-2002-2_13. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.