IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v196y2023i2d10.1007_s10957-022-02155-3.html
   My bibliography  Save this article

Inverse Problems for Double-Phase Obstacle Problems with Variable Exponents

Author

Listed:
  • Shengda Zeng

    (Yulin Normal University
    Nanjing University
    Jagiellonian University in Krakow)

  • Nikolaos S. Papageorgiou

    (National Technical University)

  • Patrick Winkert

    (Technische Universität Berlin)

Abstract

In the present paper, we are concerned with the study of a variable exponent double-phase obstacle problem which involves a nonlinear and nonhomogeneous partial differential operator, a multivalued convection term, a general multivalued boundary condition and an obstacle constraint. Under the framework of anisotropic Musielak–Orlicz Sobolev spaces, we establish the nonemptiness, boundedness and closedness of the solution set of such problems by applying a surjectivity theorem for multivalued pseudomonotone operators and the variational characterization of the first eigenvalue of the Steklov eigenvalue problem for the p-Laplacian. In the second part, we consider a nonlinear inverse problem which is formulated by a regularized optimal control problem to identify the discontinuous parameters for the variable exponent double-phase obstacle problem. We then introduce the parameter-to-solution map, study a continuous result of Kuratowski type and prove the solvability of the inverse problem.

Suggested Citation

  • Shengda Zeng & Nikolaos S. Papageorgiou & Patrick Winkert, 2023. "Inverse Problems for Double-Phase Obstacle Problems with Variable Exponents," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 666-699, February.
  • Handle: RePEc:spr:joptap:v:196:y:2023:i:2:d:10.1007_s10957-022-02155-3
    DOI: 10.1007/s10957-022-02155-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-022-02155-3
    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/s10957-022-02155-3?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:joptap:v:196:y:2023:i:2:d:10.1007_s10957-022-02155-3. 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.