IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v123y2013i12p4373-4406.html
   My bibliography  Save this article

Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces

Author

Listed:
  • Hinz, Michael
  • Röckner, Michael
  • Teplyaev, Alexander

Abstract

Starting with a regular symmetric Dirichlet form on a locally compact separable metric space X, our paper studies elements of vector analysis, Lp-spaces of vector fields and related Sobolev spaces. These tools are then employed to obtain existence and uniqueness results for some quasilinear elliptic PDE and SPDE in variational form on X by standard methods. For many of our results locality is not assumed, but most interesting applications involve local regular Dirichlet forms on fractal spaces such as nested fractals and Sierpinski carpets.

Suggested Citation

  • Hinz, Michael & Röckner, Michael & Teplyaev, Alexander, 2013. "Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4373-4406.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:12:p:4373-4406
    DOI: 10.1016/j.spa.2013.06.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414913001798
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2013.06.009?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. Liu, Xuan & Qian, Zhongmin, 2018. "Backward problems for stochastic differential equations on the Sierpinski gasket," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3387-3418.

    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:eee:spapps:v:123:y:2013:i:12:p:4373-4406. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.