IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-0348-8035-0_16.html
   My bibliography  Save this book chapter

Besov Regularity for the Neumann Problem

In: Function Spaces, Differential Operators and Nonlinear Analysis

Author

Listed:
  • Stephan Dahlke

    (Universität Bremen, Fachbereich 3 ZeTeM)

Abstract

This paper is concerned with the regularity of the solutions to the Neumann problem in Lipschitz domains SZ contained in Rd. Especially, we consider the specific scaleB r s(L (Q)) 117 = s/d + 1/p, of Besov spaces. The regularity of the variational solution in these Besov spaces determines the order of approximation that can be achieved by adaptive and nonlinear numerical schemes. We show that the solution to the Neumann problem is much smoother in the specific Besov scale than in the usual LP-Sobolev scale which justifies the use of adaptive schemes. The proofs are performed by combining some recent regularity results derived by Zanger [23] with some specific properties of harmonic Besov spaces.

Suggested Citation

  • Stephan Dahlke, 2003. "Besov Regularity for the Neumann Problem," Springer Books, in: Dorothee Haroske & Thomas Runst & Hans-Jürgen Schmeisser (ed.), Function Spaces, Differential Operators and Nonlinear Analysis, pages 267-277, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-8035-0_16
    DOI: 10.1007/978-3-0348-8035-0_16
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:sprchp:978-3-0348-8035-0_16. 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.