IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2024i1p63-d1554837.html
   My bibliography  Save this article

The Existence and Uniqueness of Nonlinear Elliptic Equations with General Growth in the Gradient

Author

Listed:
  • Angelo Alvino

    (Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, 80138 Napoli, Italy
    Current address: Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, Italy.)

  • Vincenzo Ferone

    (Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, 80138 Napoli, Italy
    Current address: Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, Italy.)

  • Anna Mercaldo

    (Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, 80138 Napoli, Italy
    Current address: Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, Italy.)

Abstract

In this paper, we prove the existence and uniqueness results for a weak solution to a class of Dirichlet boundary value problems whose prototype is − Δ p u = β | ∇ u | q + f i n Ω , u = 0 o n ∂ Ω , where Ω is a bounded open subset of R N , N ≥ 2 , 1 < p < N , Δ p u = div | ∇ u | p − 2 ∇ u , p − 1 < q < p , β is a positive constant and f is a measurable function satisfying suitable summability conditions depending on q and a smallness condition.

Suggested Citation

  • Angelo Alvino & Vincenzo Ferone & Anna Mercaldo, 2024. "The Existence and Uniqueness of Nonlinear Elliptic Equations with General Growth in the Gradient," Mathematics, MDPI, vol. 13(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:63-:d:1554837
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/1/63/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/1/63/
    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:13:y:2024:i:1:p:63-:d:1554837. 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.