IDEAS home Printed from https://ideas.repec.org/a/spr/pardea/v6y2025i1d10.1007_s42985-024-00308-9.html
   My bibliography  Save this article

Singular elliptic PDEs: an extensive overview

Author

Listed:
  • Francescantonio Oliva

    (“Sapienza” Università di Roma)

  • Francesco Petitta

    (“Sapienza” Università di Roma)

Abstract

In this survey we provide an overview of nonlinear elliptic homogeneous boundary value problems featuring singular zero-order terms with respect to the unknown variable whose prototype equation is $$ -\Delta u = {u^{-\gamma }} \ {\text {in}}\ \Omega $$ - Δ u = u - γ in Ω where $$\Omega $$ Ω is a bounded subset of $$\mathbb {R}^N$$ R N ( $$N\ge 2$$ N ≥ 2 ), and $$\gamma >0$$ γ > 0 . We start by outlining the basic concepts and the mathematical framework needed for setting the problem. Both old and new key existence and uniqueness results are presented, alongside regularity issues depending on the regularity of the data. The presentation aims to be modern, self-contained and consistent. Some examples and open problems are also discussed.

Suggested Citation

  • Francescantonio Oliva & Francesco Petitta, 2025. "Singular elliptic PDEs: an extensive overview," Partial Differential Equations and Applications, Springer, vol. 6(1), pages 1-82, March.
    • Handle: RePEc:spr:pardea:v:6:y:2025:i:1:d:10.1007_s42985-024-00308-9
    DOI: 10.1007/s42985-024-00308-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s42985-024-00308-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s42985-024-00308-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:pardea:v:6:y:2025:i:1:d:10.1007_s42985-024-00308-9. 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.