IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v108y2001i3d10.1023_a1017587408883.html
   My bibliography  Save this article

Variations of Constrained Domain Functionals Associated with Boundary-Value Problems

Author

Listed:
  • C. Huang

    (Wright State University)

  • D. Miller

    (Wright State University)

Abstract

We study variational formulas for maximizers for domain functionalsF(x0, u(x0)), x0∈Ώ, and ∫ΏF(x,u(x))dxover all Lipschitz domains Ώ satisfying the constraint∫Ώg(x) dx=1. Here, u is the solution ofa diffusion equation in Ώ. Functional variations arecomputed using domain variations which preserve the constraint exactly. Weshow that any maximizer solves a moving boundary problem for the diffusionequation. Further, we show that, for problems with symmetry, the optimaldomains Ώ are balls.

Suggested Citation

  • C. Huang & D. Miller, 2001. "Variations of Constrained Domain Functionals Associated with Boundary-Value Problems," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 587-615, March.
    • Handle: RePEc:spr:joptap:v:108:y:2001:i:3:d:10.1023_a:1017587408883
    DOI: 10.1023/A:1017587408883
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1017587408883
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1017587408883?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. D. F. Miller, 2007. "Second-Order Optimality Conditions for Constrained Domain Optimization," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 413-432, September.

    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:108:y:2001:i:3:d:10.1023_a:1017587408883. 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.