IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i7p1031-d1367222.html
   My bibliography  Save this article

Geometric Approximation of Point Interactions in Three-Dimensional Domains

Author

Listed:
  • Denis Ivanovich Borisov

    (Institute of Mathematics, Ufa Federal Research Center, Russian Academy of Sciences, Ufa 450008, Russia
    Institute of Mathematics, Informatics and Robotics, Bashkir State University, Ufa 450076, Russia
    Nikol’skii Mathematical Institute, Peoples Friendship University of Russia (RUDN University), Moscow 117198, Russia)

Abstract

In this paper, we study a three-dimensional second-order elliptic operator with a point interaction in an arbitrary domain. The operator is supposed to be self-adjoint. We cut out a small cavity around the center of the interaction and consider an operator in such perforated domain with the Robin condition on the boundary of the cavity. Our main result states that once the coefficient in this Robin condition is appropriately chosen, the operator in the perforated domain converges to that with the point interaction in the norm resolvent sense. We also succeed in establishing order-sharp estimates for the convergence rate.

Suggested Citation

  • Denis Ivanovich Borisov, 2024. "Geometric Approximation of Point Interactions in Three-Dimensional Domains," Mathematics, MDPI, vol. 12(7), pages 1-26, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1031-:d:1367222
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/7/1031/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/7/1031/
    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:12:y:2024:i:7:p:1031-:d:1367222. 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.